Bibliography C

♦A♦B♦C♦D♦E♦F♦G♦H♦I♦J♦K♦L♦M♦N♦O♦P♦Q♦R♦S♦T♦U♦V♦W♦X♦Y♦Z♦

L. G. Cabral-Rosetti and M. A. Sanchis-Lozano (2000)
Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams,

J. Comput. Appl. Math. 115 (1-2), pp. 93–99.

External Links:

ISSN 0377-0427, Document, MathReview (Lorenzo L. Salcedo), ZentralBlatt.

Referenced by:

§16.24(ii).

Encodings:

BibTeX
F. Cajori (1929)
A History of Mathematical Notations, Volume II,

Open Court Publishing Company, Chicago.

Notes:

Reprinted by Cosimo in 2007.

External Links:

ZentralBlatt.

Referenced by:

¶ ‣ §24.1.

Encodings:

BibTeX
F. Calogero (1978)
Asymptotic behaviour of the zeros of the (generalized) Laguerre polynomial ${L}_{{n}}^{{\alpha}}(x)$ as the index $\alpha\rightarrow\infty$ and limiting formula relating Laguerre polynomials of large index and large argument to Hermite polynomials,

Lett. Nuovo Cimento (2) 23 (3), pp. 101–102.

External Links:

ISSN 0024-1318, Document, MathReview (R. A. Askey).

Referenced by:

§18.7(iii).

Encodings:

BibTeX
J. Camacho, R. Guimerà and L. A. N. Amaral (2002)
Analytical solution of a model for complex food webs,

Phys. Rev. E 65 (3), pp. (030901–1)–(030901–4).

External Links:

Document.

Referenced by:

§8.24(i).

Encodings:

BibTeX
P. J. Cameron (1994)
Combinatorics: Topics, Techniques, Algorithms,

Cambridge University Press, Cambridge.

External Links:

ISBN 0-521-45133-7; 0-521-45761-0, MathReview (E. J. F. Primrose), ZentralBlatt.

Referenced by:

§26.13.

Encodings:

BibTeX
J. B. Campbell (1979)
Bessel functions $J_{\nu}(x)$ and $Y_{\nu}(x)$ of real order and real argument,

Comput. Phys. Comm. 18 (1), pp. 133–142.

Notes:

Double-precision Fortran, maximum accuracy 16S.

External Links:

ISSN 0010-4655, Document, Code.

Referenced by:

§10.77(iii).

Encodings:

BibTeX
J. B. Campbell (1980)
On Temme’s algorithm for the modified Bessel function of the third kind,

ACM Trans. Math. Software 6 (4), pp. 581–586.

External Links:

ISSN 0098-3500, Document, MathReview, ZentralBlatt.

Referenced by:

§10.74(iv).

Encodings:

BibTeX
J. B. Campbell (1981)
Bessel functions $I_{\nu}(x)$ and $K_{\nu}(x)$ of real order and complex argument,

Comput. Phys. Comm. 24 (1), pp. 97–105.

Notes:

Double-precision Fortran, maximum accuracy 16S. For erratum see same journal 25 (1982), p. 207.

External Links:

ISSN 0010-4655, Document, Code.

Referenced by:

§10.77(v).

Encodings:

BibTeX
J. B. Campbell (1984)
Determination of $\nu$ -zeros of Hankel functions,

Comput. Phys. Comm. 32 (3), pp. 333–339.

Notes:

Double-precision Fortran, maximum accuracy 7S.

External Links:

ISSN 0010-4655, Document, Code.

Referenced by:

§10.77(x).

Encodings:

BibTeX
R. Campbell (1955)
Théorie Générale de L’Équation de Mathieu et de quelques autres Équations différentielles de la mécanique,

Masson et Cie, Paris (French).

External Links:

MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

¶ ‣ §28.1.

Encodings:

BibTeX
R. G. Campos (1995)
A quadrature formula for the Hankel transform,

Numer. Algorithms 9 (2), pp. 343–354.

External Links:

ISSN 1017-1398, Document, MathReview (V. I. Polovinkin), ZentralBlatt.

Referenced by:

¶ ‣ §10.74(vii).

Encodings:

BibTeX
S. M. Candel (1981)
An algorithm for the Fourier-Bessel transform,

Comput. Phys. Comm. 23 (4), pp. 343–353.

External Links:

ISSN 0010-4655, Document, MathReview.

Referenced by:

¶ ‣ §10.74(vii).

Encodings:

BibTeX
CAOP (Web Site)
Work Group of Computational Mathematics, University of Kassel, Germany..

Notes:

Computer Algebra and Orthogonal Polynomials: a Web service using Maple for online generation of formulas and graphs of orthogonal polynomials belonging to the Askey scheme. For further information see Swarttouw (1997) and Koepf (1999).

External Links:

CAOP.

Referenced by:

§18.42.

Encodings:

BibTeX
L. Carlitz (1953)
Some congruences for the Bernoulli numbers,

Amer. J. Math. 75 (1), pp. 163–172.

External Links:

FullText, MathReview (A. L. Whiteman), ZentralBlatt.

Referenced by:

§24.10(i).

Encodings:

BibTeX
L. Carlitz (1954a)
A note on Euler numbers and polynomials,

Nagoya Math. J. 7, pp. 35–43.

External Links:

MathReview (A. L. Whiteman), ZentralBlatt.

Referenced by:

§24.10(iv).

Encodings:

BibTeX
L. Carlitz (1954b)
$q$ -Bernoulli and Eulerian numbers,

Trans. Amer. Math. Soc. 76 (2), pp. 332–350.

External Links:

FullText, MathReview (A. L. Whiteman), ZentralBlatt.

Referenced by:

¶ ‣ §17.3(iii), §24.16(iii).

Encodings:

BibTeX
L. Carlitz (1958)
Expansions of $q$ -Bernoulli numbers,

Duke Math. J. 25 (2), pp. 355–364.

External Links:

Document, MathReview (A. L. Whiteman), ZentralBlatt.

Referenced by:

¶ ‣ §17.3(iii).

Encodings:

BibTeX
L. Carlitz (1960)
Note on Nörlund’s polynomial $B_{{n}}^{{(z)}}$ ,

Proc. Amer. Math. Soc. 11 (3), pp. 452–455.

External Links:

FullText, MathReview (M. P. Drazin), ZentralBlatt.

Referenced by:

¶ ‣ §26.1, ¶ ‣ §26.1.

Encodings:

BibTeX
L. Carlitz (1961a)
A recurrence formula for $\zeta(2n)$ ,

Proc. Amer. Math. Soc. 12 (6), pp. 991–992.

External Links:

FullText, MathReview (R. D. James).

Referenced by:

§24.14(i).

Encodings:

BibTeX
L. Carlitz (1961b)
The Staudt-Clausen theorem,

Math. Mag. 34, pp. 131–146.

External Links:

MathReview (K. Goldberg), ZentralBlatt.

Referenced by:

§24.6.

Encodings:

BibTeX
L. Carlitz (1963)
The inverse of the error function,

Pacific J. Math. 13 (2), pp. 459–470.

External Links:

MathReview (D. P. Banerjee), ZentralBlatt.

Referenced by:

§7.17(ii).

Encodings:

BibTeX
R. D. Carlitz (1972)
Hadronic matter at high density,

Phys. Rev. D 5 (12), pp. 3231–3242.

External Links:

Document.

Referenced by:

¶ ‣ §5.20.

Encodings:

BibTeX
B. C. Carlson and J. FitzSimons (2000)
Reduction theorems for elliptic integrands with the square root of two quadratic factors,

J. Comput. Appl. Math. 118 (1-2), pp. 71–85.

Notes:

Code written by the second author to compute symmetric elliptic integrals numerically in the Derive computer algebra system is available.

External Links:

ISSN 0377-0427, Document, Code, MathReview, ZentralBlatt.

Referenced by:

§19.29(ii), ¶ ‣ §19.36(i), §19.36(i), §19.39(iv).

Encodings:

BibTeX
B. C. Carlson and J. L. Gustafson (1994)
Asymptotic approximations for symmetric elliptic integrals,

SIAM J. Math. Anal. 25 (2), pp. 288–303.

External Links:

ISSN 0036-1410, Document, MathReview (Bruce C. Berndt), ZentralBlatt.

Referenced by:

§19.12, §19.27(ii), §19.27(iii), §19.27(iv), §19.27(v), §19.27(vi).

Encodings:

BibTeX
B. C. Carlson and J. L. Gustafson (1985)
Asymptotic expansion of the first elliptic integral,

SIAM J. Math. Anal. 16 (5), pp. 1072–1092.

External Links:

ISSN 0036-1410, Document, MathReview (Kusum Soni), ZentralBlatt.

Referenced by:

§19.27(ii), §19.27(vi), §19.9(ii), §2.5(ii).

Encodings:

BibTeX
B. C. Carlson and E. M. Notis (1981)
Algorithm 577: Algorithm for incomplete elliptic intergrals [S21],

ACM Trans. Math. Software 7 (3), pp. 398–403.

External Links:

ISSN 0098-3500, Document, TOMS module 577 (in GAMS), ZentralBlatt.

Referenced by:

§19.39(iv).

Encodings:

BibTeX
B. C. Carlson and G. S. Rushbrooke (1950)
On the expansion of a Coulomb potential in spherical harmonics,

Proc. Cambridge Philos. Soc. 46, pp. 626–633.

External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

§34.12.

Encodings:

BibTeX
B. C. Carlson (1961a)
Ellipsoidal distributions of charge or mass,

J. Mathematical Phys. 2, pp. 441–450.

External Links:

MathReview (H. Bremekamp), ZentralBlatt.

Referenced by:

§19.33(iv), ¶ ‣ §19.37(iv).

Encodings:

BibTeX
B. C. Carlson (1961b)
Some series and bounds for incomplete elliptic integrals,

J. Math. and Phys. 40, pp. 125–134.

External Links:

MathReview (L. Robin), ZentralBlatt.

Referenced by:

§19.15, §19.9(ii).

Encodings:

BibTeX
B. C. Carlson (1963)
Lauricella’s hypergeometric function $F_{D}$ ,

J. Math. Anal. Appl. 7 (3), pp. 452–470.

External Links:

Document, MathReview (L. J. Slater), ZentralBlatt.

Referenced by:

§19.15, §19.16(iii), §19.18(ii), §19.25(vii), §19.28, §19.28.

Encodings:

BibTeX
B. C. Carlson (1964)
Normal elliptic integrals of the first and second kinds,

Duke Math. J. 31 (3), pp. 405–419.

External Links:

Document, MathReview (S. Hitotumatu), ZentralBlatt.

Referenced by:

§19.22(iii), §19.23, §19.25(vi), §19.33(i), §19.33(i).

Encodings:

BibTeX
B. C. Carlson (1965)
On computing elliptic integrals and functions,

J. Math. and Phys. 44, pp. 36–51.

External Links:

MathReview (R. Nicolovius), ZentralBlatt.

Referenced by:

§19.36(ii), §19.36(ii).

Encodings:

BibTeX
B. C. Carlson (1966)
Some inequalities for hypergeometric functions,

Proc. Amer. Math. Soc. 17 (1), pp. 32–39.

External Links:

FullText, MathReview (Gabor Szegö), ZentralBlatt.

Referenced by:

§19.24(i), §19.24(i), §19.24(ii), §19.9(i), §19.9(ii).

Encodings:

BibTeX
B. C. Carlson (1970)
Inequalities for a symmetric elliptic integral,

Proc. Amer. Math. Soc. 25 (3), pp. 698–703.

External Links:

FullText, MathReview (Y. L. Luke), ZentralBlatt.

Referenced by:

¶ ‣ §19.24(ii), §19.9(ii).

Encodings:

BibTeX
B. C. Carlson (1971)
New proof of the addition theorem for Gegenbauer polynomials,

SIAM J. Math. Anal. 2, pp. 347–351.

External Links:

ISSN 1095-7154, Document, MathReview (Mary L. Boas), ZentralBlatt.

Referenced by:

§18.18(ii).

Encodings:

BibTeX
B. C. Carlson (1972a)
An algorithm for computing logarithms and arctangents,

Math. Comp. 26 (118), pp. 543–549.

External Links:

FullText, MathReview (F. Gotze), ZentralBlatt.

Referenced by:

¶ ‣ §4.45(i).

Encodings:

BibTeX
B. C. Carlson (1976)
Quadratic transformations of Appell functions,

SIAM J. Math. Anal. 7 (2), pp. 291–304.

External Links:

Document, MathReview (L. J. Slater), ZentralBlatt.

Referenced by:

§16.16(ii), §19.22(i).

Encodings:

BibTeX
B. C. Carlson (1977a)
Elliptic integrals of the first kind,

SIAM J. Math. Anal. 8 (2), pp. 231–242.

External Links:

Document, MathReview (H. E. Fettis), ZentralBlatt.

Referenced by:

§19.29(iii).

Encodings:

BibTeX
B. C. Carlson (1978)
Short proofs of three theorems on elliptic integrals,

SIAM J. Math. Anal. 9 (3), pp. 524–528.

External Links:

Document, MathReview (Y. L. Luke), ZentralBlatt.

Referenced by:

§19.26(i).

Encodings:

BibTeX
B. C. Carlson (1979)
Computing elliptic integrals by duplication,

Numer. Math. 33 (1), pp. 1–16.

External Links:

ISSN 0029-599X, Document, MathReview, ZentralBlatt.

Referenced by:

§19.19.

Encodings:

BibTeX
B. C. Carlson (1985)
The hypergeometric function and the $R$ -function near their branch points,

Rend. Sem. Mat. Univ. Politec. Torino (Fascicolo Speciale), pp. 63–89.

External Links:

ISSN 0373-1243, MathReview (R. A. Askey), ZentralBlatt.

Referenced by:

§19.27(vi).

Encodings:

BibTeX
B. C. Carlson (1987)
A table of elliptic integrals of the second kind,

Math. Comp. 49 (180), pp. 595–606, S13–S17.

External Links:

ISSN 0025-5718, Document, Supplement, MathReview (F. W. J. Olver), ZentralBlatt.

Referenced by:

§19.29(i).

Encodings:

BibTeX
B. C. Carlson (1988)
A table of elliptic integrals of the third kind,

Math. Comp. 51 (183), pp. 267–280, S1–S5.

External Links:

ISSN 0025-5718, Document, Supplement, MathReview (F. W. J. Olver), ZentralBlatt.

Referenced by:

§19.29(i).

Encodings:

BibTeX
B. C. Carlson (1990)
Landen Transformations of Integrals,

in Asymptotic and Computational Analysis (Winnipeg, MB, 1989),

Lecture Notes in Pure and Appl. Math., Vol. 124, pp. 75–94.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§19.22(iii).

Encodings:

BibTeX
B. C. Carlson (1995)
Numerical computation of real or complex elliptic integrals,

Numer. Algorithms 10 (1-2), pp. 13–26.

External Links:

ISSN 1017-1398, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §19.36(i), ¶ ‣ §19.36(ii), §19.36(i), §19.36(i), ¶ ‣ §19.37(iv).

Encodings:

BibTeX
B. C. Carlson (1999)
Toward symbolic integration of elliptic integrals,

J. Symbolic Comput. 28 (6), pp. 739–753.

Notes:

Code written by J. FitzSimons to generate reduction tables for elliptic integrals symbolically in the Derive computer algebra system is available.

External Links:

ISSN 0747-7171, Document, Code, MathReview (Axel Riese), ZentralBlatt.

Referenced by:

§19.29(i), §19.29(ii), §19.29(ii), §19.29(ii), §19.29(ii).

Encodings:

BibTeX
B. C. Carlson (2002)
Three improvements in reduction and computation of elliptic integrals,

J. Res. Nat. Inst. Standards Tech. 107 (5), pp. 413–418.

External Links:

FullText.

Referenced by:

§19.22(ii), §19.29(ii), ¶ ‣ §19.36(i), §19.8(i).

Encodings:

BibTeX
B. C. Carlson (2004)
Symmetry in c, d, n of Jacobian elliptic functions,

J. Math. Anal. Appl. 299 (1), pp. 242–253.

External Links:

ISSN 0022-247X, Document, MathReview Entry, ZentralBlatt.

Referenced by:

§19.25(v), §19.25(v), §22.13(i), §22.6(ii), §22.6(iii), §22.8(i), §22.8(ii).

Encodings:

BibTeX
B. C. Carlson (2005)
Jacobian elliptic functions as inverses of an integral,

J. Comput. Appl. Math. 174 (2), pp. 355–359.

External Links:

ISSN 0377-0427, Document, MathReview (R. N. Kalia), ZentralBlatt.

Referenced by:

§19.25(v), §22.15(ii).

Encodings:

BibTeX
B. C. Carlson (2006a)
Some reformulated properties of Jacobian elliptic functions,

J. Math. Anal. Appl. 323 (1), pp. 522–529.

External Links:

ISSN 0022-247X, Document, MathReview Entry, ZentralBlatt.

Referenced by:

§19.25(v), §19.25(v), §22.13(i), §22.13(ii), §22.13(iii), §22.14(i), §22.14(ii).

Encodings:

BibTeX
B. C. Carlson (2006b)
Table of integrals of squared Jacobian elliptic functions and reductions of related hypergeometric $R$ -functions,

Math. Comp. 75 (255), pp. 1309–1318.

External Links:

ISSN 0025-5718, Document, MathReview, ZentralBlatt.

Referenced by:

§19.25(v), §19.29(i), §22.14(ii).

Encodings:

BibTeX
B. C. Carlson (2008)
Power series for inverse Jacobian elliptic functions,

Math. Comp. 77 (263), pp. 1615–1621.

External Links:

ISSN 0025-5718, Document, MathReview (Shaun Cooper).

Referenced by:

§19.25(v), §22.15(ii).

Encodings:

BibTeX
B. C. Carlson (2011)
Permutation symmetry for theta functions,

J. Math. Anal. Appl. 378 (1), pp. 42–48.

External Links:

ISSN 0022-247X, Document, FullText, MathReview (Mohammad Ahmad), ZentralBlatt.

Referenced by:

§20.11(v), §20.7(i), §20.7(i), §20.7(ii), §20.7(ii), §20.7(ii), §20.7(iii), §20.7(vii).

Encodings:

BibTeX
B. C. Carlson (1972b)
Intégrandes à deux formes quadratiques,

C. R. Acad. Sci. Paris Sér. A–B 274 (15 May, 1972, Sér. A), pp. 1458–1461 (French).

External Links:

MathReview (J. A. Donaldson), ZentralBlatt.

Referenced by:

§19.31.

Encodings:

BibTeX
B. C. Carlson (1977b)
Special Functions of Applied Mathematics,

Academic Press, New York.

External Links:

ISBN 0-12-160150-1, MathReview, ZentralBlatt.

Referenced by:

§19.16(ii), §19.16(ii), §19.16(iii), §19.18(i), §19.18(ii), §19.2(iv), §19.20(i), §19.20(iv), §19.20(v), §19.21(ii), §19.21(ii), §19.23, §19.25(i), §19.26(i), §19.26(iii), §19.28, §19.30(i), §19.30(ii), §19.30(iii), §19.32, §19.33(i), §19.33(ii), §19.33(iv), §19.34, Ch.19, §5.12, §5.6(ii), Ch.5, Bille C. Carlson.

Encodings:

BibTeX
B. C. Carlson (1998)
Elliptic Integrals: Symmetry and Symbolic Integration,

in Tricomi’s Ideas and Contemporary Applied Mathematics (Rome/Turin, 1997),

Atti dei Convegni Lincei, Vol. 147, pp. 161–181.

External Links:

MathReview (S. L. Kalla), ZentralBlatt.

Referenced by:

§19.26(iii), §19.29(i).

Encodings:

BibTeX
M. Carmignani and A. Tortorici Macaluso (1985)
Calcolo delle funzioni speciali $\Gamma(x)$ , $\mathop{\mathrm{log}\/}\nolimits\Gamma(x)$ , $\beta(x,y)$ , $\mathop{\mathrm{erf}\/}\nolimits(x)$ , $\mathop{\mathrm{erfc}\/}\nolimits(x)$ alle alte precisioni,

Atti Accad. Sci. Lett. Arti Palermo Ser. (5) 2(1981/82) (1), pp. 7–25 (Italian).

Notes:

Translated title: Computation of the special functions $\Gamma(x),\;{\rm log}\,\Gamma(x),\;\beta(x,y),\;{\rm erf}\,(x),\;{\rm erfc}\,(x)$ to a high degree of precision

External Links:

MathReview, ZentralBlatt.

Referenced by:

§5.24(ii).

Encodings:

BibTeX
L. D. Carr, C. W. Clark and W. P. Reinhardt (2000)
Stationary solutions of the one-dimensional nonlinear Schrödinger equation. I. Case of repulsive nonlinearity,

Phys. Rev. A 62 (063610), pp. 1–10.

External Links:

Document.

Referenced by:

§22.19(iii).

Encodings:

BibTeX
H. S. Carslaw and J. C. Jaeger (1959)
Conduction of Heat in Solids,

2nd edition, Clarendon Press, Oxford.

External Links:

ISBN 0198533039.

Referenced by:

§7.21, Ch.7.

Encodings:

BibTeX
H. S. Carslaw (1930)
Introduction to the Theory of Fourier’s Series and Integrals,

3rd edition, Macmillan, London.

Notes:

Reprinted by Dover, New York, 1950.

External Links:

ZentralBlatt.

Referenced by:

§6.16(i).

Encodings:

BibTeX
J. R. Cash and R. V. M. Zahar (1994)
A Unified Approach to Recurrence Algorithms,

in Approximation and Computation (West Lafayette, IN, 1993),

International Series of Computational Mathematics, Vol. 119, pp. 97–120.

External Links:

ISBN 0-8176-3753-2, MathReview (R. M. M. Mattheij), ZentralBlatt.

Referenced by:

§3.6(vii).

Encodings:

BibTeX
A. Cayley (1895)
An Elementary Treatise on Elliptic Functions,

George Bell and Sons, London.

Notes:

Republished by Dover Publications, Inc,, New York, 1961. Table erratum: Math. Comp. v. 29 (1975), no. 130, p. 670.

External Links:

ZentralBlatt.

Referenced by:

§19.12, Ch.19.

Encodings:

BibTeX
R. Cazenave (1969)
Intégrales et Fonctions Elliptiques en Vue des Applications,

Préface de Henri Villat. Publications Scientifiques et Techniques du Ministère de l’Air, No. 452, Centre de Documentation de l’Armement, Paris.

External Links:

MathReview (B. Ć. Carlson).

Referenced by:

§19.11(i), §19.12, §19.14(i), ¶ ‣ §19.36(ii), §19.4(ii), §19.8(ii), §19.8(iii), Ch.19.

Encodings:

BibTeX
CEPHES (free C library)

Notes:

This library treats about 180 different mathematical functions, including a substantial collection of probability integrals, Bessel functions, and higher transcendental functions. Implementations in single, double, and quad precisions are provided. See Moshier (1989).

External Links:

Package CEPHES (in GAMS).

Referenced by:

§ ‣ § Software Cross Index.

Encodings:

BibTeX
H. H. Chan (1998)
On Ramanujan’s cubic transformation formula for $\mathop{{{}_{{2}}F_{{1}}}\/}\nolimits\!\left(\frac{1}{3},\frac{2}{3};1;z\right)$ ,

Math. Proc. Cambridge Philos. Soc. 124 (2), pp. 193–204.

External Links:

ISSN 0305-0041, Document, MathReview (Aleksander Grytczuk), ZentralBlatt.

Referenced by:

§15.8(v).

Encodings:

BibTeX
S. Chandrasekhar (1984)
The Mathematical Theory of Black Holes,

in General Relativity and Gravitation (Padova, 1983),

pp. 5–26.

External Links:

MathReview Entry.

Referenced by:

§31.17(ii).

Encodings:

BibTeX
F. Chapeau-Blondeau and A. Monir (2002)
Numerical evaluation of the Lambert $W$ function and application to generation of generalized Gaussian noise with exponent 1/2,

IEEE Trans. Signal Process. 50 (9), pp. 2160–2165.

External Links:

ISSN 1053-587X, Document, MathReview (J. Borwein).

Referenced by:

§4.44, §4.45(iii).

Encodings:

BibTeX
C. J. Chapman (1999)
Caustics in cylindrical ducts,

Proc. Roy. Soc. London Ser. A 455, pp. 2529–2548.

External Links:

ISSN 1364-5021, Document, MathReview, ZentralBlatt.

Referenced by:

§36.14(iv).

Encodings:

BibTeX
B. W. Char (1980)
On Stieltjes’ continued fraction for the gamma function,

Math. Comp. 34 (150), pp. 547–551.

External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt.

Referenced by:

§5.10.

Encodings:

BibTeX
R. Chattamvelli and R. Shanmugam (1997)
Algorithm AS 310. Computing the non-central beta distribution function,

Appl. Statist. 46 (1), pp. 146–156.

Notes:

Single-precision Fortran.

External Links:

FullText, Code, ZentralBlatt.

Referenced by:

§8.28(iv).

Encodings:

BibTeX
M. A. Chaudhry, N. M. Temme and E. J. M. Veling (1996)
Asymptotics and closed form of a generalized incomplete gamma function,

J. Comput. Appl. Math. 67 (2), pp. 371–379.

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt.

Referenced by:

§8.16.

Encodings:

BibTeX
M. A. Chaudhry and S. M. Zubair (1994)
Generalized incomplete gamma functions with applications,

J. Comput. Appl. Math. 55 (1), pp. 99–124.

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt.

Referenced by:

§8.16.

Encodings:

BibTeX
M. A. Chaudhry and S. M. Zubair (2001)
On a Class of Incomplete Gamma Functions with Applications,

Chapman & Hall/CRC, Boca Raton, FL.

External Links:

ISBN 1-58488-143-7, MathReview (R. K. Raina), ZentralBlatt.

Referenced by:

§8.16.

Encodings:

BibTeX
T. W. Chaundy (1969)
Elementary Differential Equations,

Clarendon Press, Oxford.

External Links:

ISBN 0-19-853139-7, MathReview, ZentralBlatt.

Referenced by:

§16.12.

Encodings:

BibTeX
A. D. Chave (1983)
Numerical integration of related Hankel transforms by quadrature and continued fraction expansion,

Geophysics 48 (12), pp. 1671–1686.

Notes:

Fortran code.

External Links:

ISSN 0098-3500, Document.

Referenced by:

§10.77(ix).

Encodings:

BibTeX
P. L. Chebyshev (1851)
Sur la fonction qui détermine la totalité des nombres premiers inférieurs à une limite donnée,

Mem. Ac. Sc. St. Pétersbourg 6, pp. 141–157.

Referenced by:

§25.16(i).

Encodings:

BibTeX
M. Chellali (1988)
Accélération de calcul de nombres de Bernoulli,

J. Number Theory 28 (3), pp. 347–362 (French).

External Links:

ISSN 0022-314X, Document, MathReview (Louis Shapiro), ZentralBlatt.

Referenced by:

§24.19(i).

Encodings:

BibTeX
R. Chelluri, L. B. Richmond and N. M. Temme (2000)
Asymptotic estimates for generalized Stirling numbers,

Analysis (Munich) 20 (1), pp. 1–13.

External Links:

ISSN 0174-4747, MathReview (F. T. Howard), ZentralBlatt.

Referenced by:

§26.8(vii).

Encodings:

BibTeX
J. Chen (1966)
On the representation of a large even integer as the sum of a prime and the product of at most two primes,

Kexue Tongbao (Foreign Lang. Ed.) 17, pp. 385–386.

External Links:

MathReview (T. Hayashida).

Referenced by:

§27.13(ii).

Encodings:

BibTeX
L. Chen, M. E. H. Ismail and P. Simeonov (1999)
Asymptotics of Racah coefficients and polynomials,

J. Phys. A 32 (3), pp. 537–553.

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt.

Referenced by:

§34.8, §34.8.

Encodings:

BibTeX
Y. Chen and M. E. H. Ismail (1998)
Asymptotics of the largest zeros of some orthogonal polynomials,

J. Phys. A 31 (25), pp. 5525–5544.

External Links:

ISSN 0305-4470, Document, MathReview (Tim H. Baker), ZentralBlatt.

Referenced by:

§18.26(v), §18.29.

Encodings:

BibTeX
E. W. Cheney (1982)
Introduction to Approximation Theory,

2nd edition, Chelsea Publishing Co., New York.

Notes:

Reprinted by AMS Chelsea Publishing, Providence, RI, 1998

External Links:

ISBN 0-8218-1374-9, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §18.38(i).

Encodings:

BibTeX
I. Cherednik (1995)
Macdonald’s evaluation conjectures and difference Fourier transform,

Invent. Math. 122 (1), pp. 119–145.

Notes:

Erratum: see same journal 125(1996), no. 2, p. 391.

External Links:

ISSN 0020-9910, Document, MathReview (Eric M. Opdam), ZentralBlatt.

Referenced by:

¶ ‣ §17.14.

Encodings:

BibTeX
T. M. Cherry (1948)
Expansions in terms of parabolic cylinder functions,

Proc. Edinburgh Math. Soc. (2) 8, pp. 50–65.

External Links:

MathReview (I. I. Hirschman, Jr.), ZentralBlatt.

Referenced by:

§12.16.

Encodings:

BibTeX
C. Chester, B. Friedman and F. Ursell (1957)
An extension of the method of steepest descents,

Proc. Cambridge Philos. Soc. 53, pp. 599–611.

External Links:

MathReview (P. Henrici), ZentralBlatt.

Referenced by:

§2.4(v).

Encodings:

BibTeX
C. Chiccoli, S. Lorenzutta and G. Maino (1987)
A numerical method for generalized exponential integrals,

Comput. Math. Appl. 14 (4), pp. 261–268.

External Links:

ISSN 0898-1221, MathReview (R. P. Boas), ZentralBlatt.

Referenced by:

§8.25(v).

Encodings:

BibTeX
C. Chiccoli, S. Lorenzutta and G. Maino (1988)
On the evaluation of generalized exponential integrals ${E}_{v}(x)$ ,

J. Comput. Phys. 78 (2), pp. 278–287.

External Links:

ISSN 0021-9991, Document, MathReview, ZentralBlatt.

Referenced by:

§8.25(v), §8.26(iv).

Encodings:

BibTeX
C. Chiccoli, S. Lorenzutta and G. Maino (1990a)
An algorithm for exponential integrals of real order,

Computing 45 (3), pp. 269–276.

Notes:

Includes Fortran code

External Links:

ISSN 0010-485X, Document, MathReview, ZentralBlatt.

Referenced by:

§8.25(v), §8.28(vi).

Encodings:

BibTeX
C. Chiccoli, S. Lorenzutta and G. Maino (1990b)
On a Tricomi series representation for the generalized exponential integral,

Internat. J. Comput. Math. 31, pp. 257–262.

Notes:

Includes Fortran code

External Links:

Document, ZentralBlatt.

Referenced by:

§8.28(vi).

Encodings:

BibTeX
L. Chihara (1987)
On the zeros of the Askey-Wilson polynomials, with applications to coding theory,

SIAM J. Math. Anal. 18 (1), pp. 191–207.

External Links:

ISSN 0036-1410, Document, MathReview (Mourad E. H. Ismail), ZentralBlatt.

Referenced by:

¶ ‣ §18.38(iii).

Encodings:

BibTeX
T. S. Chihara (1978)
An Introduction to Orthogonal Polynomials,

Mathematics and its Applications, Vol. 13, Gordon and Breach Science Publishers, New York.

External Links:

ISBN 0-677-04150-0, MathReview (A. G. Law), ZentralBlatt.

Referenced by:

§18.2(iii), §18.2(iv), §18.20(i), ¶ ‣ §18.30, §18.30, Ch.18.

Encodings:

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T. S. Chihara and M. E. H. Ismail (1993)
Extremal measures for a system of orthogonal polynomials,

Constr. Approx. 9, pp. 111–119.

External Links:

ISSN 0176-4276, Document, MathReview (Mizan Rahman), ZentralBlatt.

Referenced by:

§18.28(iv).

Encodings:

BibTeX
Y. Chikuse (2003)
Statistics on Special Manifolds,

Lecture Notes in Statistics, Vol. 174, Springer-Verlag, New York.

External Links:

ISBN 0-387-00160-3, MathReview (M. Hušková), ZentralBlatt.

Referenced by:

§35.9.

Encodings:

BibTeX
R. C. Y. Chin and G. W. Hedstrom (1978)
A dispersion analysis for difference schemes: Tables of generalized Airy functions,

Math. Comp. 32 (144), pp. 1163–1170.

External Links:

ISSN 0025-5718, FullText, MathReview (Philip Brenner), ZentralBlatt.

Referenced by:

§9.13(ii).

Encodings:

BibTeX
B. K. Choudhury (1995)
The Riemann zeta-function and its derivatives,

Proc. Roy. Soc. London Ser. A 450, pp. 477–499.

External Links:

ISSN 0962-8444, FullText, MathReview, ZentralBlatt.

Referenced by:

§25.18(i).

Encodings:

BibTeX
Y. Chow, L. Gatteschi and R. Wong (1994)
A Bernstein-type inequality for the Jacobi polynomial,

Proc. Amer. Math. Soc. 121 (3), pp. 703–709.

External Links:

ISSN 0002-9939, FullText, MathReview (Joaquin Bustoz), ZentralBlatt.

Referenced by:

§18.14(i).

Encodings:

BibTeX
N. B. Christensen (1990)
Optimized fast Hankel transform filters,

Geophysical Prospecting 38 (5), pp. 545–568.

External Links:

Document.

Referenced by:

¶ ‣ §10.74(vii).

Encodings:

BibTeX
J. S. Christiansen and M. E. H. Ismail (2006)
A moment problem and a family of integral evaluations,

Trans. Amer. Math. Soc. 358 (9), pp. 4071–4097.

External Links:

ISSN 0002-9947, Document, MathReview (Roelof Koekoek), ZentralBlatt.

Referenced by:

§18.28(iv).

Encodings:

BibTeX
J. A. Christley and I. J. Thompson (1994)
CRCWFN: Coupled real Coulomb wavefunctions,

Comput. Phys. Comm. 79 (1), pp. 143–155.

Notes:

Double-precision Fortran code.

External Links:

ISSN 0010-4655, Document, Code, ZentralBlatt.

Referenced by:

§33.26(ii).

Encodings:

BibTeX
R. F. Christy and I. Duck (1961)
$\gamma$ rays from an extranuclear direct capture process,

Nuclear Physics 24 (1), pp. 89–101.

External Links:

Document.

Referenced by:

§33.22(v).

Encodings:

BibTeX
G. Chrystal (1959)
Algebra: An Elementary Textbook for the Higher Classes of Secondary Schools and for Colleges,

6th edition, Vol. 1, Chelsea Publishing Co., New York.

Notes:

A seventh edition (reprinting of the sixth edition) was published by AMS Chelsea Publishing Series, American Mathematical Society, 1964.

External Links:

ISBN 0-8218-1648-9, SeventhEdition, MathReview, ZentralBlatt.

Referenced by:

§1.2(i), §1.2(ii), §1.2(iii).

Encodings:

BibTeX
D. V. Chudnovsky and G. V. Chudnovsky (1988)
Approximations and Complex Multiplication According to Ramanujan,

in Ramanujan Revisited (Urbana-Champaign, Ill., 1987),

(R. A. Askey, B. C. Bernd, K. G. Ramanathan and R. A. Rankin Eds.), pp. 375–472.

External Links:

MathReview (Maurice Mignotte), ZentralBlatt.

Referenced by:

§20.11(iii).

Encodings:

BibTeX
C. K. Chui (1988)
Multivariate Splines,

CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 54, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

Notes:

With an appendix by Harvey Diamond

External Links:

ISBN 0-89871-226-2, MathReview (B. Boyanov), ZentralBlatt.

Referenced by:

§3.11(vi).

Encodings:

BibTeX
A. Ciarkowski (1989)
Uniform asymptotic expansion of an integral with a saddle point, a pole and a branch point,

Proc. Roy. Soc. London Ser. A 426, pp. 273–286.

External Links:

ISSN 0080-4630, FullText, MathReview, ZentralBlatt.

Referenced by:

§2.4(vi).

Encodings:

BibTeX
R. Cicchetti and A. Faraone (2004)
Incomplete Hankel and modified Bessel functions: A class of special functions for electromagnetics,

IEEE Trans. Antennas and Propagation 52 (12), pp. 3373–3389.

External Links:

ISSN 0018-926X, Document, MathReview (T. Erber).

Referenced by:

§10.46.

Encodings:

BibTeX

G. M. Cicuta and E. Montaldi (1975)
Remarks on the full asymptotic expansion of Feynman parametrized integrals,

Lett. Nuovo Cimento (2) 13 (8), pp. 310–312.

External Links:

MathReview (R. A. Askey).

Referenced by:

§2.3(iii).

Encodings:

BibTeX
C. W. Clark (1979)
Coulomb phase shift,

American Journal of Physics 47 (8), pp. 683–684.

External Links:

Document.

Referenced by:

¶ ‣ §5.20.

Encodings:

BibTeX
A. P. Clarke and W. Marwood (1984)
A compact mathematical function package,

Australian Computer Journal 16 (3), pp. 107–114.

Notes:

Includes Pascal function evaluation package

External Links:

ISSN 0004-8917, ZentralBlatt.

Referenced by:

§16.27(ii).

Encodings:

BibTeX
F. Clarke (1989)
The universal von Staudt theorems,

Trans. Amer. Math. Soc. 315 (2), pp. 591–603.

External Links:

ISSN 0002-9947, FullText, MathReview (T. Metsänkylä), ZentralBlatt.

Referenced by:

§24.16(iii).

Encodings:

BibTeX
P. A. Clarkson and E. L. Mansfield (2003)
The second Painlevé equation, its hierarchy and associated special polynomials,

Nonlinearity 16 (3), pp. R1–R26.

External Links:

ISSN 0951-7715, Document, MathReview (Andrei A. Kapaev), ZentralBlatt.

Referenced by:

§32.8(ii).

Encodings:

BibTeX
P. A. Clarkson and J. B. McLeod (1988)
A connection formula for the second Painlevé transcendent,

Arch. Rational Mech. Anal. 103 (2), pp. 97–138.

External Links:

ISSN 0945-8396, Document, MathReview (Reinhard Schäfke), ZentralBlatt.

Referenced by:

§32.11(ii).

Encodings:

BibTeX
P. A. Clarkson (1991)
Nonclassical Symmetry Reductions and Exact Solutions for Physically Significant Nonlinear Evolution Equations,

in Nonlinear and Chaotic Phenomena in Plasmas, Solids and Fluids (Edmonton, AB, 1990),

(J. A. Tuszynski Ed.), pp. 72–79.

External Links:

MathReview.

Referenced by:

§29.19(ii).

Encodings:

BibTeX
P. A. Clarkson (2003a)
The third Painlevé equation and associated special polynomials,

J. Phys. A 36 (36), pp. 9507–9532.

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt.

Referenced by:

§32.8(iii), §32.9(i).

Encodings:

BibTeX
P. A. Clarkson (2003b)
The fourth Painlevé equation and associated special polynomials,

J. Math. Phys. 44 (11), pp. 5350–5374.

External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt.

Referenced by:

§32.8(iv).

Encodings:

BibTeX
P. A. Clarkson (2005)
Special polynomials associated with rational solutions of the fifth Painlevé equation,

J. Comput. Appl. Math. 178 (1-2), pp. 111–129.

External Links:

ISSN 0377-0427, Document, MathReview (Davide Batic), ZentralBlatt.

Referenced by:

§32.8(v), §32.9(ii).

Encodings:

BibTeX
P. A. Clarkson (2006)
Painlevé Equations—Nonlinear Special Functions: Computation and Application,

in Orthogonal Polynomials and Special Functions,

(W. van Assche Ed.), Lecture Notes in Math., Vol. 1883, pp. 331–411.

External Links:

ISBN 3-540-31062-2, MathReview (Marta Mazzocco), ZentralBlatt.

Referenced by:

Ch.32.

Encodings:

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T. Clausen (1828)
Über die Fälle, wenn die Reihe von der Form $y=1+\frac{\alpha}{1}\cdot\frac{\beta}{\gamma}x+\frac{\alpha\cdot\alpha+1}{1\cdot 2}\cdot\frac{\beta\cdot\beta+1}{\gamma\cdot\gamma+1}x^{2}+$ etc. ein Quadrat von der Form $z=1+\frac{\alpha^{{\prime}}}{1}\cdot\frac{\beta^{{\prime}}}{\gamma^{{\prime}}}\cdot\frac{\delta^{{\prime}}}{\epsilon^{{\prime}}}x+\frac{\alpha^{{\prime}}\cdot\alpha^{{\prime}}+1}{1\cdot 2}\cdot\frac{\beta^{{\prime}}\cdot\beta^{{\prime}}+1}{\gamma^{{\prime}}\cdot\gamma^{{\prime}}+1}\cdot\frac{\delta^{{\prime}}\cdot\delta^{{\prime}}+1}{\epsilon^{{\prime}}\cdot\epsilon^{{\prime}}+1}x^{2}+$ etc. hat,

J. Reine Angew. Math. 3, pp. 89–91.

External Links:

ZentralBlatt.

Referenced by:

§16.12.

Encodings:

BibTeX
D. S. Clemm (1969)
Algorithm 352: Characteristic values and associated solutions of Mathieu’s differential equation,

Comm. ACM 12 (7), pp. 399–407.

Notes:

Includes double-precision Fortran program, maximum accuracy 13D.

External Links:

ISSN 0001-0782, Document.

Referenced by:

§28.36(ii), §28.36(iii).

Encodings:

BibTeX
W. W. Clendenin (1966)
A method for numerical calculation of Fourier integrals,

Numer. Math. 8 (5), pp. 422–436.

External Links:

ISSN 0029-599X, Document, MathReview (M. P. S. Madan), ZentralBlatt.

Referenced by:

§3.5(vii).

Encodings:

BibTeX
C. W. Clenshaw and A. R. Curtis (1960)
A method for numerical integration on an automatic copmputer,

Numer. Math. 2 (4), pp. 197–205.

External Links:

ISSN 0029-599X, Document, MathReview (A. H. Stroud), ZentralBlatt.

Referenced by:

§3.5(iv).

Encodings:

BibTeX
C. W. Clenshaw, D. W. Lozier, F. W. J. Olver and P. R. Turner (1986)
Generalized exponential and logarithmic functions,

Comput. Math. Appl. Part B 12 (5-6), pp. 1091–1101.

External Links:

ISSN 0886-9561, MathReview (M. E. Muldoon), ZentralBlatt.

Referenced by:

§4.12.

Encodings:

BibTeX
C. W. Clenshaw, G. F. Miller and M. Woodger (1962)
Algorithms for special functions. I,

Numer. Math. 4, pp. 403–419.

External Links:

ISSN 0029-599X, Document, MathReview (A. S. Householder), ZentralBlatt.

Referenced by:

§5.24(ii).

Encodings:

BibTeX
C. W. Clenshaw, F. W. J. Olver and P. R. Turner (1989)
Level-Index Arithmetic: An Introductory Survey,

in Numerical Analysis and Parallel Processing (Lancaster, 1987),

Lecture Notes in Math., Vol. 1397, pp. 95–168.

External Links:

MathReview Entry, ZentralBlatt.

Referenced by:

§3.1(iv).

Encodings:

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C. W. Clenshaw and F. W. J. Olver (1984)
Beyond floating point,

J. Assoc. Comput. Mach. 31 (2), pp. 319–328.

External Links:

Document, MathReview Entry, ZentralBlatt.

Referenced by:

§3.1(iv).

Encodings:

BibTeX
C. W. Clenshaw (1955)
A note on the summation of Chebyshev series,

Math. Tables Aids Comput. 9 (51), pp. 118–120.

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

§18.40.

Encodings:

BibTeX
C. W. Clenshaw (1957)
The numerical solution of linear differential equations in Chebyshev series,

Proc. Cambridge Philos. Soc. 53 (1), pp. 134–149.

External Links:

MathReview (L. Fox), ZentralBlatt.

Referenced by:

¶ ‣ §18.38(i), ¶ ‣ §3.11(ii).

Encodings:

BibTeX
C. W. Clenshaw (1962)
Chebyshev Series for Mathematical Functions,

National Physical Laboratory Mathematical Tables, Vol. 5. Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London.

External Links:

MathReview (L. J. Slater), ZentralBlatt.

Referenced by:

¶ ‣ §3.11(ii), §4.47(i), §5.23(ii), §6.20(ii).

Encodings:

BibTeX
L. D. Cloutman (1989)
Numerical evaluation of the Fermi-Dirac integrals,

The Astrophysical Journal Supplement Series 71, pp. 677–699.

Notes:

Double-precision Fortran, maximum precision 12D.

External Links:

ISSN 0067-0049, Document, Code.

Referenced by:

§25.12(iii), §25.18(i), §25.19, §25.21(vii).

Encodings:

BibTeX
J. A. Cochran and J. N. Hoffspiegel (1970)
Numerical techniques for finding $\nu$ -zeros of Hankel functions,

Math. Comp. 24 (110), pp. 413–422.

External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt.

Referenced by:

§10.21(xiv).

Encodings:

BibTeX
J. A. Cochran (1963)
Further formulas for calculating approximate values of the zeros of certain combinations of Bessel functions,

IEEE Trans. Microwave Theory Tech. 11 (6), pp. 546–547.

External Links:

ISSN 0018-9480, FullText.

Referenced by:

§10.21(x).

Encodings:

BibTeX
J. A. Cochran (1964)
Remarks on the zeros of cross-product Bessel functions,

J. Soc. Indust. Appl. Math. 12 (3), pp. 580–587.

External Links:

Document, MathReview (M. J. O. Strutt), ZentralBlatt.

Referenced by:

§10.21(x), §10.21(x).

Encodings:

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J. A. Cochran (1965)
The zeros of Hankel functions as functions of their order,

Numer. Math. 7 (3), pp. 238–250.

External Links:

ISSN 0029-599X, Document, MathReview (F. W. J. Olver), ZentralBlatt.

Referenced by:

§10.21(xiv).

Encodings:

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J. A. Cochran (1966a)
The analyticity of cross-product Bessel function zeros,

Proc. Cambridge Philos. Soc. 62, pp. 215–226.

External Links:

MathReview (R. G. Langebartel), ZentralBlatt.

Referenced by:

§10.21(x).

Encodings:

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J. A. Cochran (1966b)
The asymptotic nature of zeros of cross-product Bessel functions,

Quart. J. Mech. Appl. Math. 19 (4), pp. 511–522.

External Links:

ISSN 0033-5614, Document, MathReview (F. W. J. Olver), ZentralBlatt.

Referenced by:

§10.21(x).

Encodings:

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W. J. Cody, K. E. Hillstrom and H. C. Thacher (1971)
Chebyshev approximations for the Riemann zeta function,

Math. Comp. 25 (115), pp. 537–547.

External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt.

Referenced by:

§25.20.

Encodings:

BibTeX
W. J. Cody and K. E. Hillstrom (1967)
Chebyshev approximations for the natural logarithm of the gamma function,

Math. Comp. 21 (98), pp. 198–203.

External Links:

FullText, ZentralBlatt.

Referenced by:

§5.23(i).

Encodings:

BibTeX
W. J. Cody and K. E. Hillstrom (1970)
Chebyshev approximations for the Coulomb phase shift,

Math. Comp. 24 (111), pp. 671–677.

Notes:

Corrigendum: same journal, 26(1972), p. 1031.

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

§33.25.

Encodings:

BibTeX
W. J. Cody, K. A. Paciorek and H. C. Thacher (1970)
Chebyshev approximations for Dawson’s integral,

Math. Comp. 24 (109), pp. 171–178.

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

§7.24(i).

Encodings:

BibTeX
W. J. Cody, A. J. Strecok and H. C. Thacher (1973)
Chebyshev approximations for the psi function,

Math. Comp. 27 (121), pp. 123–127.

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

§5.23(i).

Encodings:

BibTeX
W. J. Cody and H. C. Thacher (1968)
Rational Chebyshev approximations for the exponential integral $\mathop{E_{1}\/}\nolimits(x)$ ,

Math. Comp. 22 (103), pp. 641–649.

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

§6.20(i).

Encodings:

BibTeX
W. J. Cody and H. C. Thacher (1969)
Chebyshev approximations for the exponential integral $\mathop{\mathrm{Ei}\/}\nolimits(x)$ ,

Math. Comp. 23 (106), pp. 289–303.

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

§6.13, §6.20(i).

Encodings:

BibTeX
W. J. Cody and W. Waite (1980)
Software Manual for the Elementary Functions,

Prentice-Hall, Englewood Cliffs.

External Links:

ISBN 0138220646, ZentralBlatt.

Referenced by:

¶ ‣ §4.45(i).

Encodings:

BibTeX
W. J. Cody (1965a)
Chebyshev approximations for the complete elliptic integrals $K$ and $E$ ,

Math. Comp. 19 (89), pp. 105–112.

External Links:

FullText, MathReview (G. N. Lance), ZentralBlatt.

Referenced by:

§19.38.

Encodings:

BibTeX
W. J. Cody (1965b)
Chebyshev polynomial expansions of complete elliptic integrals,

Math. Comp. 19 (90), pp. 249–259.

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

§19.38.

Encodings:

BibTeX
W. J. Cody (1968)
Chebyshev approximations for the Fresnel integrals,

Math. Comp. 22 (102), pp. 450–453.

Notes:

with Microfiche Supplement

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

§7.24(i).

Encodings:

BibTeX
W. J. Cody (1969)
Rational Chebyshev approximations for the error function,

Math. Comp. 23 (107), pp. 631–637.

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

§7.24(i).

Encodings:

BibTeX
W. J. Cody (1970)
A survey of practical rational and polynomial approximation of functions,

SIAM Rev. 12 (3), pp. 400–423.

External Links:

Document, MathReview (J. H. Curtiss), ZentralBlatt.

Referenced by:

§3.11(i).

Encodings:

BibTeX
W. J. Cody (1983)
Algorithm 597: Sequence of modified Bessel functions of the first kind,

ACM Trans. Math. Software 9 (2), pp. 242–245.

Notes:

Double-precision Fortran, maximum accuracy 24S.

External Links:

ISSN 0098-3500, Document, TOMS module 597 (in GAMS), ZentralBlatt.

Referenced by:

§10.77(iii).

Encodings:

BibTeX
W. J. Cody (1991)
Performance evaluation of programs related to the real gamma function,

ACM Trans. Math. Software 17 (1), pp. 46–54.

External Links:

ISSN 0098-3500, Document, MathReview, ZentralBlatt.

Referenced by:

§5.24(ii), §5.24(iii).

Encodings:

BibTeX
W. J. Cody (1993a)
Algorithm 714: CELEFUNT – A portable test package for complex elementary functions,

ACM Trans. Math. Software 19 (1), pp. 1–21.

External Links:

ISSN 0098-3500, Document, TOMS module 714 (in GAMS), ZentralBlatt.

Referenced by:

§4.48(v).

Encodings:

BibTeX
W. J. Cody (1993b)
Algorithm 715: SPECFUN – A portable FORTRAN package of special function routines and test drivers,

ACM Trans. Math. Software 19 (1), pp. 22–32.

Notes:

Double precision, maximum accuracy 18S.

External Links:

ISSN 0098-3500, Document, Remark. TOMS module 715 (in GAMS), ZentralBlatt.

Referenced by:

§10.77(ii), §10.77(iii), §5.24(ii), §5.24(iii), §6.21(ii), §7.25(ii), §7.25(vi).

Encodings:

BibTeX
M. W. Coffey (2008)
On some series representations of the Hurwitz zeta function,

J. Comput. Appl. Math. 216 (1), pp. 297–305.

External Links:

ISSN 0377-0427, Document, FullText, MathReview Entry, ZentralBlatt.

Referenced by:

§25.11(iv), §25.11(iv).

Encodings:

BibTeX
M. W. Coffey (2009)
An efficient algorithm for the Hurwitz zeta and related functions,

J. Comput. Appl. Math. 225 (2), pp. 338–346.

External Links:

ISSN 0377-0427, Document, FullText, MathReview Entry, ZentralBlatt.

Referenced by:

§25.18(i), §25.18(i).

Encodings:

BibTeX
H. Cohen (1993)
A Course in Computational Algebraic Number Theory,

Springer-Verlag, Berlin-New York.

External Links:

ISBN 3-540-55640-0, 0-387-55640-0, MathReview (Joe P. Buhler), ZentralBlatt.

Referenced by:

§23.17(i), §27.18, §27.18.

Encodings:

BibTeX
J. P. Coleman and A. J. Monaghan (1983)
Chebyshev expansions for the Bessel function $J_{{n}}(z)$ in the complex plane,

Math. Comp. 40 (161), pp. 343–366.

External Links:

ISSN 0025-5718, FullText, MathReview (C. W. Clenshaw), ZentralBlatt.

Referenced by:

¶ ‣ §10.76(ii).

Encodings:

BibTeX
J. P. Coleman (1980)
A Fortran subroutine for the Bessel function $J_{n}(x)$ of order 0 to 10,

Comput. Phys. Comm. 21 (1), pp. 109–118.

Notes:

Double-precision Fortran, maximum accuracy 16S.

External Links:

ISSN 0010-4655, Document, Code.

Referenced by:

§10.77(ii).

Encodings:

BibTeX
J. P. Coleman (1987)
Polynomial approximations in the complex plane,

J. Comput. Appl. Math. 18 (2), pp. 193–211.

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §10.76(ii).

Encodings:

BibTeX
L. Collatz (1960)
The Numerical Treatment of Differential Equations,

3rd edition, Die Grundlehren der Mathematischen Wissenschaften, Vol. 60, Springer, Berlin.

Notes:

Translated by P. G. Williams from a supplemented version of the 2d German edition

External Links:

MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §3.4(iii), ¶ ‣ §3.4(i).

Encodings:

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D. Colton and R. Kress (1998)
Inverse Acoustic and Electromagnetic Scattering Theory,

2nd edition, Applied Mathematical Sciences, Vol. 93, Springer-Verlag, Berlin.

External Links:

ISBN 3-540-62838-X, MathReview, ZentralBlatt.

Referenced by:

§10.73(i).

Encodings:

BibTeX
Combinatorial Object Server (Web Site)
Department of Computer Science, University of Victoria, Canada..

Notes:

Permutations, set and integer partitions, sequences, graphs, and trees.

External Links:

Combinatorial Object Server.

Referenced by:

§26.22.

Encodings:

BibTeX
L. Comtet (1974)
Advanced Combinatorics: The Art of Finite and Infinite Expansions,

enlarged edition, D. Reidel Publishing Co., Dordrecht.

Notes:

Revised and enlarged English translation by D. Reidel of Analyse Combinatoire, Tomes I, II, Presses Universitaires de France, Paris, 1970.

External Links:

ISBN 90-277-0441-4, MathReview, ZentralBlatt.

Referenced by:

§26.3(i), §26.3(iii), §26.3(iv), §26.3(v), §26.4(i), §26.4(ii), §26.4(iii), §26.5(i), §26.5(ii), §26.5(iii), §26.6(i), §26.6(ii), §26.6(iii), §26.7(i), §26.7(ii), §26.7(iii), §26.8(i), §26.8(ii), §26.8(iv), §26.8(v), Ch.26.

Encodings:

BibTeX
S. Conde and S. L. Kalla (1979)
The $\nu$ -zeros of $J_{{-\nu}}(x)$ ,

Math. Comp. 33 (145), pp. 423–426.

External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt.

Referenced by:

§10.21(xiv).

Encodings:

BibTeX
S. Conde and S. L. Kalla (1981)
On zeros of the hypergeometric function,

Serdica 7 (3), pp. 243–249.

External Links:

ISSN 0204-4140, MathReview (R. G. Buschman), ZentralBlatt.

Referenced by:

§15.13.

Encodings:

BibTeX
E. U. Condon and G. H. Shortley (1935)
The Theory of Atomic Spectra,

Cambridge University Press, Cambridge.

Notes:

Reprinted with corrections in 1991. Transferred to digital reprinting, 1999.

External Links:

ISBN 0-521-04713-7; 0-521-09209-4, ZentralBlatt.

Referenced by:

§34.1.

Encodings:

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W. C. Connett, C. Markett and A. L. Schwartz (1993)
Product formulas and convolutions for angular and radial spheroidal wave functions,

Trans. Amer. Math. Soc. 338 (2), pp. 695–710.

External Links:

ISSN 0002-9947, FullText, MathReview (Jean-Claude Lucquiaud), ZentralBlatt.

Referenced by:

§30.10, §30.11(vi).

Encodings:

BibTeX
J. N. L. Connor, P. R. Curtis and D. Farrelly (1983)
A differential equation method for the numerical evaluation of the Airy, Pearcey and swallowtail canonical integrals and their derivatives,

Molecular Phys. 48 (6), pp. 1305–1330.

External Links:

ISSN 0026-8976, Document, MathReview (Peter Giblin).

Referenced by:

§36.10(i), §36.10(ii), §36.15(v), §36.8.

Encodings:

BibTeX
J. N. L. Connor and P. R. Curtis (1982)
A method for the numerical evaluation of the oscillatory integrals associated with the cuspoid catastrophes: Application to Pearcey’s integral and its derivatives,

J. Phys. A 15 (4), pp. 1179–1190.

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt.

Referenced by:

§36.15(iii), §36.8.

Encodings:

BibTeX
J. N. L. Connor and D. Farrelly (1981)
Molecular collisions and cusp catastrophes: Three methods for the calculation of Pearcey’s integral and its derivatives,

Chem. Phys. Lett. 81 (2), pp. 306–310.

External Links:

ISSN 0009-2614, Document, MathReview (J. S. Joel).

Referenced by:

§36.14(iii).

Encodings:

BibTeX
J. N. L. Connor and D. C. Mackay (1979)
Calculation of angular distributions in complex angular momentum theories of elastic scattering,

Molecular Physics 37 (6), pp. 1703–1712.

External Links:

Document.

Referenced by:

§14.31(iii).

Encodings:

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J. N. L. Connor (1973)
Evaluation of multidimensional canonical integrals in semiclassical collision theory,

Molecular Phys. 26 (6), pp. 1371–1377.

External Links:

Document.

Referenced by:

§36.8.

Encodings:

BibTeX
J. N. L. Connor (1974)
Semiclassical theory of molecular collisions: Many nearly coincident classical trajectories,

Molecular Phys. 27 (4), pp. 853–866.

External Links:

Document.

Referenced by:

§36.14(iii).

Encodings:

BibTeX
J. N. L. Connor (1976)
Catastrophes and molecular collisions,

Molecular Phys. 31 (1), pp. 33–55.

External Links:

Document, MathReview (V. M. Zakaljukin).

Referenced by:

§36.14(iii).

Encodings:

BibTeX
A. G. Constantine (1963)
Some non-central distribution problems in multivariate analysis,

Ann. Math. Statist. 34 (4), pp. 1270–1285.

External Links:

FullText, MathReview (I. Olkin), ZentralBlatt.

Referenced by:

§35.4(i), §35.4(ii).

Encodings:

BibTeX
E. D. Constantinides and R. J. Marhefka (1993)
Efficient and accurate computation of the incomplete Airy functions,

Radio Science 28 (4), pp. 441–457.

External Links:

ISSN 0048-6604, Document.

Referenced by:

§9.14.

Encodings:

BibTeX
J. W. Cooley and J. W. Tukey (1965)
An algorithm for the machine calculation of complex Fourier series,

Math. Comp. 19 (90), pp. 297–301.

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §3.11(v).

Encodings:

BibTeX
R. Cools (2003)
An encyclopaedia of cubature formulas,

J. Complexity 19 (3), pp. 445–453.

Notes:

Numerical integration and its complexity (Oberwolfach, 2001)

External Links:

ISSN 0885-064X, Document, Web Page, MathReview, ZentralBlatt.

Referenced by:

§3.5(x).

Encodings:

BibTeX
F. Cooper, A. Khare and A. Saxena (2006)
Exact elliptic compactons in generalized Korteweg-de Vries equations,

Complexity 11 (6), pp. 30–34.

External Links:

ISSN 1076-2787, Document, MathReview.

Referenced by:

§19.6(i).

Encodings:

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M. D. Cooper, R. H. Jeppesen and M. B. Johnson (1979)
Coulomb effects in the Klein-Gordon equation for pions,

Phys. Rev. C 20 (2), pp. 696–704.

External Links:

Document.

Referenced by:

§33.22(vii).

Encodings:

BibTeX
R. B. Cooper (1981)
Introduction to Queueing Theory,

2nd edition, North-Holland Publishing Co., New York.

External Links:

ISBN 0-444-00379-7, FullText, MathReview, ZentralBlatt.

Referenced by:

§8.23.

Encodings:

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E. T. Copson (1933)
An approximation connected with $e^{{-x}}$ ,

Proc. Edinburgh Math. Soc. (2) 3, pp. 201–206.

External Links:

Document, ZentralBlatt.

Referenced by:

§8.11(v).

Encodings:

BibTeX
E. T. Copson (1935)
An Introduction to the Theory of Functions of a Complex Variable,

Oxford University Press, Oxford.

External Links:

ZentralBlatt.

Referenced by:

§1.10(i), §1.10(ii), §1.10(iii), §1.10(iv), §1.10(vii), §1.10(viii), §1.9(i), §1.9(ii), §1.9(iii), §1.9(v), §1.9(vi), §1.9(vii), ¶ ‣ §20.1, §22.8(iii), Ch.22, Ch.23, §4.18, §4.26(iii), §4.40(iii), Ch.4.

Encodings:

BibTeX
E. T. Copson (1963)
On the asymptotic expansion of Airy’s integral,

Proc. Glasgow Math. Assoc. 6, pp. 113–115.

External Links:

MathReview (L. Berg), ZentralBlatt.

Referenced by:

§9.5(ii).

Encodings:

BibTeX
E. T. Copson (1965)
Asymptotic Expansions,

Cambridge Tracts in Mathematics and Mathematical Physics, Cambridge University Press, New York.

External Links:

MathReview (A. E. Danese), ZentralBlatt.

Referenced by:

Ch.2.

Encodings:

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R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey and D. E. Knuth (1996)
On the Lambert $W$ function,

Adv. Comput. Math. 5 (4), pp. 329–359.

External Links:

ISSN 1019-7168, MathReview, ZentralBlatt.

Referenced by:

§4.13, §4.44, §4.44.

Encodings:

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R. M. Corless, D. J. Jeffrey and H. Rasmussen (1992)
Numerical evaluation of Airy functions with complex arguments,

J. Comput. Phys. 99 (1), pp. 106–114.

External Links:

ISSN 0021-9991, Document, MathReview, ZentralBlatt.

Referenced by:

§9.18(iv), §9.19(iii).

Encodings:

BibTeX
G. Cornell, J. H. Silverman and G. Stevens (Eds.) (1997)
Modular Forms and Fermat’s Last Theorem,

Springer-Verlag, New York.

External Links:

ISBN 0-387-94609-8; 0-387-98998-6, MathReview (M. Ram Murty), ZentralBlatt.

Referenced by:

§23.20(v).

Encodings:

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H. Cornille and A. Martin (1972)
Constraints on the phase of scattering amplitudes due to positivity,

Nuclear Phys. B 49, pp. 413–440.

External Links:

Document.

Referenced by:

§18.39(ii).

Encodings:

BibTeX
H. Cornille and A. Martin (1974)
Constraints on the phases of helicity amplitudes due to positivity,

Nuclear Phys. B 77, pp. 141–162.

External Links:

Document, MathReview.

Referenced by:

§18.39(ii).

Encodings:

BibTeX
P. Cornille (1972)
Computation of Hankel transforms,

SIAM Rev. 14 (2), pp. 278–285.

External Links:

ISSN 1095-7200, Document, MathReview (R. D. Riess), ZentralBlatt.

Referenced by:

¶ ‣ §10.74(vii).

Encodings:

BibTeX
M. S. Corrington (1961)
Applications of the complex exponential integral,

Math. Comp. 15 (73), pp. 1–6.

External Links:

FullText, MathReview (J. C. P. Miller), ZentralBlatt.

Referenced by:

§6.7(iv).

Encodings:

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C. M. Cosgrove (2006)
Chazy’s second-degree Painlevé equations,

J. Phys. A 39 (39), pp. 11955–11971.

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt.

Referenced by:

§32.7(vii).

Encodings:

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O. Costin (1999)
Correlation between pole location and asymptotic behavior for Painlevé I solutions,

Comm. Pure Appl. Math. 52 (4), pp. 461–478.

External Links:

ISSN 0010-3640, FullText, MathReview (Alexander Vladimirovich Kitaev), ZentralBlatt.

Referenced by:

§32.12(i).

Encodings:

BibTeX
CoStLy (free C-XSC library)

Notes:

Complex interval standard function library. For details see Neher (2007)

External Links:

CoStLy.

Referenced by:

§ ‣ § Software Cross Index, M. Neher (2007).

Encodings:

BibTeX
D. A. Cox (1984)
The arithmetic-geometric mean of Gauss,

Enseign. Math. (2) 30 (3-4), pp. 275–330.

External Links:

ISSN 0013-8584, MathReview (Bruce C. Berndt), ZentralBlatt.

Referenced by:

§19.8(i).

Encodings:

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D. A. Cox (1985)
Gauss and the arithmetic-geometric mean,

Notices Amer. Math. Soc. 32 (2), pp. 147–151.

External Links:

ISSN 0002-9920, MathReview (Willard Parker).

Referenced by:

§19.8(i).

Encodings:

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R. E. Crandall (1996)
Topics in Advanced Scientific Computation,

TELOS/Springer-Verlag, New York.

External Links:

ISBN 0-387-94473-7, MathReview (Ian Gladwell), ZentralBlatt.

Referenced by:

§24.19(ii), §24.19(ii).

Encodings:

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R. Crandall and C. Pomerance (2005)
Prime Numbers: A Computational Perspective,

2nd edition, Springer-Verlag, New York.

External Links:

ISBN 978-0-387-25282-7; 0-387-25282-7, MathReview (Robert Juricevic), ZentralBlatt.

Referenced by:

¶ ‣ §27.12, §27.12, §27.18, §27.18, §27.18, §27.18, §27.18, §27.18, §27.19, §27.19, §27.19.

Encodings:

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J. E. Cremona (1997)
Algorithms for Modular Elliptic Curves,

2nd edition, Cambridge University Press, Cambridge.

External Links:

ISBN 0-521-59820-6, MathReview (Joseph H. Silverman), ZentralBlatt.

Referenced by:

§23.20(ii).

Encodings:

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J. Crisóstomo, S. Lepe and J. Saavedra (2004)
Quasinormal modes of the extremal BTZ black hole,

Classical Quantum Gravity 21 (12), pp. 2801–2809.

External Links:

ISSN 0264-9381, MathReview (Donato Bini), ZentralBlatt.

Referenced by:

§13.28(iii).

Encodings:

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D. C. Cronemeyer (1991)
Demagnetization factors for general ellipsoids,

J. Appl. Phys. 70 (6), pp. 2911–2914.

Notes:

For an erratum concerning availability of tables, see J. Appl. Phys 70(1991)7660.

External Links:

Document.

Referenced by:

§19.15, §19.33(iii).

Encodings:

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B. Crstici and Gh. Tudor (1975)
Compléments au traité de D. S. Mitrinović. VII. Sur une inégalité de D. S. Mitrinović,

Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. (498-541), pp. 153–154.

External Links:

MathReview (D. C. Benson), ZentralBlatt.

Referenced by:

§7.8.

Encodings:

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A. Cruz, J. Esparza and J. Sesma (1991)
Zeros of the Hankel function of real order out of the principal Riemann sheet,

J. Comput. Appl. Math. 37 (1-3), pp. 89–99.

External Links:

ISSN 0377-0427, Document, MathReview (Boro Döring), ZentralBlatt.

Referenced by:

§10.21(ix).

Encodings:

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A. Cruz and J. Sesma (1982)
Zeros of the Hankel function of real order and of its derivative,

Math. Comp. 39 (160), pp. 639–645.

External Links:

ISSN 0025-5718, FullText, MathReview (S. Ahmed), ZentralBlatt.

Referenced by:

§10.21(ix).

Encodings:

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A. Csótó and G. M. Hale (1997)
$S$ -matrix and $R$ -matrix determination of the low-energy ${}^{{5}}\mathrm{He}$ and ${}^{{5}}\mathrm{Li}$ resonance parameters,

Phys. Rev. C 55 (1), pp. 536–539.

External Links:

Document.

Referenced by:

§33.22(vii).

Encodings:

BibTeX
Cunningham Project (Web Site)

Notes:

Seeks to factor numbers of the form $b^{n}\pm 1$ for $b=2,3,5,6,7,10,11,12$ .

External Links:

Home Page.

Referenced by:

§27.22.

Encodings:

BibTeX
S. W. Cunningham (1969)
Algorithm AS 24: From normal integral to deviate,

Appl. Statist. 18 (3), pp. 290–293.

Notes:

Includes Fortran program, maximum accuracy 12D.

External Links:

FullText.

Referenced by:

§7.25(ii).

Encodings:

BibTeX
A. R. Curtis (1964a)
Coulomb Wave Functions,

Roy. Soc. Math. Tables, Vol. 11, Cambridge University Press, Cambridge.

External Links:

ISBN 0-521-06156-3, MathReview (John Todd), ZentralBlatt.

Referenced by:

¶ ‣ §33.1, §33.14(i), §33.20(iv), §33.21(ii), §33.23(vi), §33.24, §33.9(ii).

Encodings:

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A. R. Curtis (1964b)
Tables of Jacobian Elliptic Functions Whose Arguments are Rational Fractions of the Quarter Period,

National Physical Laboratory Mathematical Tables, Vol. 7, Her Majesty’s Stationery Office, London.

External Links:

ISBN 00-791-1158-0, MathReview (John Todd), ZentralBlatt.

Referenced by:

§22.20(vii), §22.21.

Encodings:

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A. Cuyt, V. B. Petersen, B. Verdonk, H. Waadeland and W. B. Jones (2008)
Handbook of Continued Fractions for Special Functions,

Springer, New York.

External Links:

ISBN 978-1-4020-6948-2, MathReview Entry, ZentralBlatt.

Referenced by:

§10.10, §10.33, §10.55, §10.74(v), §12.6, §13.17, §13.5, §15.7, §16.4(iv), §17.6(vi), ¶ ‣ §17.7(ii), ¶ ‣ §18.13, ¶ ‣ §3.10(ii), ¶ ‣ §3.10(iii), §4.25, §4.39, §4.9(i), §4.9(ii), §4.9(iii), §5.10, §5.15, §6.9, §7.18(v), §7.22(i), §7.9, §8.17(v), §8.19(vii), §8.9.

Encodings:

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D. Cvijović and J. Klinowski (1994)
On the integration of incomplete elliptic integrals,

Proc. Roy. Soc. London Ser. A 444, pp. 525–532.

External Links:

ISSN 0962-8444, FullText, MathReview, ZentralBlatt.

Referenced by:

§19.13(i), §19.13(ii).

Encodings:

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D. Cvijović and J. Klinowski (1999)
Integrals involving complete elliptic integrals,

J. Comput. Appl. Math. 106 (1), pp. 169–175.

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt.

Referenced by:

§19.13(i).

Encodings:

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