Bibliography F

♦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♦

B. R. Fabijonas, D. W. Lozier and F. W. J. Olver (2004)
Computation of complex Airy functions and their zeros using asymptotics and the differential equation,

ACM Trans. Math. Software 30 (4), pp. 471–490.

External Links:

ISSN 0098-3500, Document, MathReview, ZentralBlatt.

Referenced by:

§9.17(ii), §9.17(v), §9.8(iv).

Encodings:

BibTeX
B. R. Fabijonas, D. W. Lozier and J. M. Rappoport (2003)
Algorithms and codes for the Macdonald function: Recent progress and comparisons,

J. Comput. Appl. Math. 161 (1), pp. 179–192.

External Links:

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

Referenced by:

§10.77(vi).

Encodings:

BibTeX
B. R. Fabijonas (2004)
Algorithm 838: Airy functions,

ACM Trans. Math. Software 30 (4), pp. 491–501.

Notes:

Single- and double-precision Fortran, maximum accuracy 32S.

External Links:

ISSN 0098-3500, Document, Code, MathReview Entry, ZentralBlatt.

Referenced by:

§9.20(ii), §9.20(iii), §9.20(iv).

Encodings:

BibTeX
B. R. Fabijonas and F. W. J. Olver (1999)
On the reversion of an asymptotic expansion and the zeros of the Airy functions,

SIAM Rev. 41 (4), pp. 762–773.

External Links:

ISSN 1095-7200, Document, MathReview (Eberhard Wagner), ZentralBlatt.

Referenced by:

¶ ‣ §2.2, §2.2, §3.8(v), §9.9(iv), §9.9(iv).

Encodings:

BibTeX
V. N. Faddeeva and N. M. Terent’ev (1954)
Tablicy značeniĭ funkcii $w(z)=e^{{-z^{{2}}}}(1+\frac{2i}{\sqrt{\pi}}\int^{z}_{0}e^{{t^{{2}}}}dt)$ ot kompleksnogo argumenta,

Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow (Russian).

Notes:

In Russian. English translation, see Faddeyeva and Terent’ev (1961)

External Links:

MathReview (John Todd), ZentralBlatt.

Referenced by:

§7.21.

Encodings:

BibTeX
V. N. Faddeyeva and N. M. Terent’ev (1961)
Tables of Values of the Function $w(z)=e^{{-z^{{2}}}}(1+2i\pi^{{-1/2}}\int _{{0}}^{{z}}e^{{t^{{2}}}}dt)$ for Complex Argument,

Edited by V. A. Fok; translated from the Russian by D. G. Fry. Mathematical Tables Series, Vol. 11, Pergamon Press, Oxford.

External Links:

MathReview, ZentralBlatt.

Referenced by:

V. N. Faddeeva and N. M. Terent’ev (1954).

Encodings:

BibTeX
M. Faierman (1992)
Generalized parabolic cylinder functions,

Asymptotic Anal. 5 (6), pp. 517–531.

External Links:

ISSN 0921-7134, MathReview (Wolfgang Bühring), ZentralBlatt.

Referenced by:

§12.15.

Encodings:

BibTeX
P. Falloon (2001)
Theory and Computation of Spheroidal Harmonics with General Arguments,

Master’s Thesis, The University of Western Australia, Department of Physics.

Notes:

Contains Mathematica package for spheroidal wave functions of complex arguments with complex parameters.

External Links:

FullText.

Referenced by:

§30.12, §30.18(ii), §30.18(iii).

Encodings:

BibTeX
D. F. Fang and J. F. Shriner (1992)
A computer program for the calculation of angular-momentum coupling coefficients,

Comput. Phys. Comm. 70 (1), pp. 147–153.

Notes:

Fortran for exact calculation using integers

External Links:

ISSN 0010-4655, Document, Code, MathReview Entry.

Referenced by:

§34.13, §34.13, §34.15.

Encodings:

BibTeX
J. Faraut and A. Korányi (1994)
Analysis on Symmetric Cones,

Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, Oxford-New York.

External Links:

ISBN 0-19-853477-9, MathReview (Hong Ming Ding), ZentralBlatt.

Referenced by:

§35.1, §35.4(i), §35.7(i), §35.7(iii), ¶ ‣ §35.8(i), §35.8(iv), §35.8(v), §35.8(v), Ch.35.

Encodings:

BibTeX
R. H. Farrell (1985)
Multivariate Calculation. Use of the Continuous Groups.,

Springer Series in Statistics, Springer-Verlag, New York.

External Links:

ISBN 0-387-96049-X, MathReview (Yasuko Chikuse), ZentralBlatt.

Referenced by:

§35.9.

Encodings:

BibTeX
J. D. Fay (1973)
Theta Functions on Riemann Surfaces,

Springer-Verlag, Berlin.

Notes:

Lecture Notes in Mathematics, Vol. 352

External Links:

MathReview (H. M. Farkas), ZentralBlatt.

Referenced by:

§21.1, §21.7(ii), Ch.21.

Encodings:

BibTeX
FDLIBM (free C library)

Notes:

The “Freely Distributable LIBM” package provides implementations of standard elementary functions plus a few higher functions, e.g. gamma. Double precision, maximum accuracy 20S. Developed by Sun Microsystems.

External Links:

Package FDLIBM (in GAMS).

Referenced by:

§ ‣ § Software Cross Index.

Encodings:

BibTeX
M. V. Fedoryuk (1989)
The Lamé wave equation,

Uspekhi Mat. Nauk 44 (1(265)), pp. 123–144, 248 (Russian).

Notes:

In Russian. English translation: Russian Math. Surveys, 44(1989), no. 1, pp. 153–180

External Links:

ISSN 0042-1316, Document, MathReview (R. G. Langebartel), ZentralBlatt.

Referenced by:

§29.11.

Encodings:

BibTeX
M. V. Fedoryuk (1991)
Asymptotics of the spectrum of the Heun equation and of Heun functions,

Izv. Akad. Nauk SSSR Ser. Mat. 55 (3), pp. 631–646 (Russian).

Notes:

In Russian. English translation: Math. USSR-Izv., 38(1992), no. 3, pp. 621–635 (1992)

External Links:

ISSN 0373-2436, Document, MathReview (Andreĭ Bolibrukh), ZentralBlatt.

Referenced by:

§31.13.

Encodings:

BibTeX
S. Fempl (1960)
Sur certaines sommes des intégral-cosinus,

Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).

External Links:

MathReview (L. Carlitz), ZentralBlatt.

Referenced by:

§6.15.

Encodings:

BibTeX
C. Ferreira, J. L. López and E. Pérez Sinusía (2005)
Incomplete gamma functions for large values of their variables,

Adv. in Appl. Math. 34 (3), pp. 467–485.

External Links:

ISSN 0196-8858, Document, MathReview (Boro Döring), ZentralBlatt.

Referenced by:

§8.12.

Encodings:

BibTeX
C. Ferreira and J. L. López (2001)
An asymptotic expansion of the double gamma function,

J. Approx. Theory 111 (2), pp. 298–314.

External Links:

ISSN 0021-9045, Document, MathReview (C. M. Joshi), ZentralBlatt.

Referenced by:

§5.17.

Encodings:

BibTeX
E. M. Ferreira and J. Sesma (2008)
Zeros of the Macdonald function of complex order,

J. Comput. Appl. Math. 211 (2), pp. 223–231.

External Links:

ISSN 0377-0427, Document, FullText, MathReview (Eugenia N. Petropoulou), ZentralBlatt.

Referenced by:

§10.42, §10.42.

Encodings:

BibTeX
H. E. Fettis, J. C. Caslin and K. R. Cramer (1973)
Complex zeros of the error function and of the complementary error function,

Math. Comp. 27 (122), pp. 401–407.

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

§7.13(i), §7.13(ii), §7.23(iv).

Encodings:

BibTeX
H. E. Fettis and J. C. Caslin (1964)
Tables of Elliptic Integrals of the First, Second, and Third Kind,

Technical report

Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.

Notes:

Reviewed in Math. Comp. v. 1919(1965)509. Table erratum: Math. Comp. v. 20 (1966), no. 96, pp. 639-640.

Referenced by:

¶ ‣ §19.37(ii), ¶ ‣ §19.37(ii), ¶ ‣ §19.37(iii), ¶ ‣ §19.37(iii), ¶ ‣ §19.37(iii).

Encodings:

BibTeX
H. E. Fettis and J. C. Caslin (1969)
A Table of the Complete Elliptic Integral of the First Kind for Complex Values of the Modulus. Part I,

Technical report

Technical Report ARL 69-0172, Aerospace Research Laboratories, Office of Aerospace Research, Wright-Patterson Air Force Base, Ohio.

Notes:

Table erratum: Math. Comp. v. 36 (1981), no. 153, p. 318. Part II of this report, with the same date but numbered ARL 69-0173, again puts $k=R\mathop{\exp\/}\nolimits(i\theta)$ but with $R$ as parameter and $\theta$ as variable instead of the other way around. Part III, dated May 1970 and numbered ARL 70-0081, contains tables of auxiliary functions to help interpolation.

External Links:

MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §19.36(ii), ¶ ‣ §19.37(ii).

Encodings:

BibTeX
H. E. Fettis and J. C. Caslin (1973)
Table errata; Complex zeros of Fresnel integrals,

Math. Comp. 27 (121), pp. 219.

Notes:

Errata in Abramowitz and Stegun (1964)

External Links:

FullText, MathReview.

Referenced by:

(7.13.6), §7.13(iii).

Encodings:

BibTeX
H. E. Fettis (1965)
Calculation of elliptic integrals of the third kind by means of Gauss’ transformation,

Math. Comp. 19 (89), pp. 97–104.

External Links:

FullText, MathReview (J. E. L. Peck), ZentralBlatt.

Referenced by:

¶ ‣ §19.36(ii).

Encodings:

BibTeX
H. E. Fettis (1970)
On the reciprocal modulus relation for elliptic integrals,

SIAM J. Math. Anal. 1 (4), pp. 524–526.

External Links:

Document, MathReview (B. C. Carlson), ZentralBlatt.

Referenced by:

¶ ‣ §19.7(i).

Encodings:

BibTeX
H. E. Fettis (1976)
Complex roots of $\mathop{\sin\/}\nolimits z=az$ , $\mathop{\cos\/}\nolimits z=az$ , and $\mathop{\cosh\/}\nolimits z=az$ ,

Math. Comp. 30 (135), pp. 541–545.

External Links:

FullText, MathReview (Gerhard Merz), ZentralBlatt.

Referenced by:

§4.46.

Encodings:

BibTeX
F. Feuillebois (1991)
Numerical calculation of singular integrals related to Hankel transform,

Comput. Math. Appl. 21 (2-3), pp. 87–94.

Notes:

Fortran, minimum precision 6D.

External Links:

ISSN 0898-1221, Document, MathReview, ZentralBlatt.

Referenced by:

§10.77(ix).

Encodings:

BibTeX
J. L. Fields and Y. L. Luke (1963a)
Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. II,

J. Math. Anal. Appl. 7 (3), pp. 440–451.

External Links:

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

Referenced by:

§16.11(iii).

Encodings:

BibTeX
J. L. Fields and Y. L. Luke (1963b)
Asymptotic expansions of a class of hypergeometric polynomials with respect to the order,

J. Math. Anal. Appl. 6 (3), pp. 394–403.

External Links:

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

Referenced by:

§16.11(iii).

Encodings:

BibTeX
J. L. Fields and J. Wimp (1961)
Expansions of hypergeometric functions in hypergeometric functions.,

Math. Comp. 15 (76), pp. 390–395.

External Links:

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

Referenced by:

§16.10.

Encodings:

BibTeX
J. L. Fields (1965)
Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. III,

J. Math. Anal. Appl. 12 (3), pp. 593–601.

External Links:

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

Referenced by:

§16.11(iii).

Encodings:

BibTeX
J. L. Fields (1973)
Uniform asymptotic expansions of certain classes of Meijer $G$ -functions for a large parameter,

SIAM J. Math. Anal. 4 (3), pp. 482–507.

External Links:

Document, MathReview (C. M. Joshi), ZentralBlatt.

Referenced by:

§16.22.

Encodings:

BibTeX
J. L. Fields (1983)
Uniform asymptotic expansions of a class of Meijer $G$ -functions for a large parameter,

SIAM J. Math. Anal. 14 (6), pp. 1204–1253.

External Links:

ISSN 0036-1410, Document, MathReview (Roop N. Kesarwani), ZentralBlatt.

Referenced by:

§16.22.

Encodings:

BibTeX
A. M. S. Filho and G. Schwachheim (1967)
Algorithm 309. Gamma function with arbitrary precision,

Comm. ACM 10 (8), pp. 511–512.

External Links:

ISSN 0001-0782, Document.

Referenced by:

§5.24(ii).

Encodings:

BibTeX
S. Fillebrown (1992)
Faster computation of Bernoulli numbers,

J. Algorithms 13 (3), pp. 431–445.

External Links:

ISSN 0196-6774, MathReview (P. K. Subramanian), ZentralBlatt.

Referenced by:

§24.19(i).

Encodings:

BibTeX
S. R. Finch (2003)
Mathematical Constants,

Encyclopedia of Mathematics and its Applications, Vol. 94, Cambridge University Press, Cambridge.

External Links:

ISBN 0-521-81805-2, MathReview (E. J. Barbeau), ZentralBlatt.

Referenced by:

§3.12.

Encodings:

BibTeX
N. J. Fine (1988)
Basic Hypergeometric Series and Applications,

Mathematical Surveys and Monographs, Vol. 27, American Mathematical Society, Providence, RI.

Notes:

With a foreword by George E. Andrews

External Links:

ISBN 0-8218-1524-5, MathReview (David M. Bressoud), ZentralBlatt.

Referenced by:

§17.1, §17.16, §17.6(ii), Ch.17.

Encodings:

BibTeX
G. D. Finn and D. Mugglestone (1965)
Tables of the line broadening function $H(a,v)$ ,

Monthly Notices Roy. Astronom. Soc. 129, pp. 221–235.

External Links:

FullText.

Referenced by:

§7.19(i), §7.23(ii).

Encodings:

BibTeX
P. Flajolet and A. Odlyzko (1990)
Singularity analysis of generating functions,

SIAM J. Discrete Math. 3 (2), pp. 216–240.

External Links:

ISSN 0895-4801, Document, MathReview (E. Rodney Canfield), ZentralBlatt.

Referenced by:

¶ ‣ §2.10(iv).

Encodings:

BibTeX
P. Flajolet and B. Salvy (1998)
Euler sums and contour integral representations,

Experiment. Math. 7 (1), pp. 15–35.

External Links:

ISSN 1058-6458, Link, MathReview (Bruce C. Berndt), ZentralBlatt.

Referenced by:

§25.16(ii).

Encodings:

BibTeX
C. Flammer (1957)
Spheroidal Wave Functions,

Stanford University Press, Stanford, CA.

External Links:

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

Referenced by:

¶ ‣ §30.1, §30.10, §30.17, Ch.30.

Encodings:

BibTeX
H. Flaschka and A. C. Newell (1980)
Monodromy- and spectrum-preserving deformations. I,

Comm. Math. Phys. 76 (1), pp. 65–116.

External Links:

ISSN 0010-3616, Link, MathReview (Hélène Airault), ZentralBlatt.

Referenced by:

§32.10(ii), §32.4(iii), §32.8(ii).

Encodings:

BibTeX
A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie (1962)
An Index of Mathematical Tables. Vols. I, II,

2nd edition, Published for Scientific Computing Service Ltd., London, by Addison-Wesley Publishing Co., Inc., Reading, MA.

Notes:

Table errata: Math. Comp. v.27 (1973), p. 1009.

External Links:

MathReview.

Referenced by:

§10.75(i), §11.14(i), §12.19, §13.30, §14.33, §18.41(iii), §19.37(i), §20.15, §22.21, §23.23, §24.20, §25.19, §28.35(iv), §30.17, §33.24, §4.23(viii), §4.46, §5.22(i), §6.19(i), §7.23(i), §8.26(i), §9.18(i).

Encodings:

BibTeX
A. Fletcher (1948)
Guide to tables of elliptic functions,

Math. Tables and Other Aids to Computation 3 (24), pp. 229–281.

External Links:

FullText, MathReview (S. C. van Veen).

Referenced by:

§19.37(i).

Encodings:

BibTeX
N. Fleury and A. Turbiner (1994)
Polynomial relations in the Heisenberg algebra,

J. Math. Phys. 35 (11), pp. 6144–6149.

External Links:

ISSN 0022-2488, Document, MathReview (Shao-Ming Fei), ZentralBlatt.

Referenced by:

§13.3(ii), §15.5(i), §16.3(i).

Encodings:

BibTeX

J. P. M. Flude (1998)
The Edmonds asymptotic formulas for the $3j$ and $6j$ symbols,

J. Math. Phys. 39 (7), pp. 3906–3915.

External Links:

ISSN 0022-2488, Document, MathReview (A. J. Coleman), ZentralBlatt.

Referenced by:

§34.8.

Encodings:

BibTeX
FN (free Fortran library)

Notes:

This library treats more than 100 mathematical functions. Implementations in single and double precision are provided. See Fullerton (1977).

External Links:

Package FN (in GAMS).

Referenced by:

§ ‣ § Software Cross Index.

Encodings:

BibTeX
V. A. Fock (1965)
Electromagnetic Diffraction and Propagation Problems,

International Series of Monographs on Electromagnetic Waves, Vol. 1, Pergamon Press, Oxford.

External Links:

MathReview (R. F. Millar).

Referenced by:

§9.16.

Encodings:

BibTeX
V. Fock (1945)
Diffraction of radio waves around the earth’s surface,

Acad. Sci. USSR. J. Phys. 9, pp. 255–266.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§9.1.

Encodings:

BibTeX
A. S. Fokas and M. J. Ablowitz (1982)
On a unified approach to transformations and elementary solutions of Painlevé equations,

J. Math. Phys. 23 (11), pp. 2033–2042.

External Links:

ISSN 0022-2488, Document, MathReview (Hélène Airault), ZentralBlatt.

Referenced by:

§32.13(i), §32.7(i), §32.7(iii).

Encodings:

BibTeX
A. S. Fokas, B. Grammaticos and A. Ramani (1993)
From continuous to discrete Painlevé equations,

J. Math. Anal. Appl. 180 (2), pp. 342–360.

External Links:

ISSN 0022-247X, Document, MathReview (Evangelos Ifantis), ZentralBlatt.

Referenced by:

§32.7(ii).

Encodings:

BibTeX
A. S. Fokas, A. R. Its and A. V. Kitaev (1991)
Discrete Painlevé equations and their appearance in quantum gravity,

Comm. Math. Phys. 142 (2), pp. 313–344.

External Links:

ISSN 0010-3616, Link, MathReview (Nikolai A. Kostov), ZentralBlatt.

Referenced by:

§32.15.

Encodings:

BibTeX
A. S. Fokas, A. R. Its and X. Zhou (1992)
Continuous and Discrete Painlevé Equations,

in Painlevé Transcendents: Their Asymptotics and Physical Applications,

(P. Winternitz Ed.), NATO Adv. Sci. Inst. Ser. B Phys., Vol. 278, pp. 33–47.

Notes:

Proc. NATO Adv. Res. Workshop, Sainte-Adèle, Canada, 1990

External Links:

MathReview (F. Pempinelli), ZentralBlatt.

Referenced by:

§32.15.

Encodings:

BibTeX
A. S. Fokas and Y. C. Yortsos (1981)
The transformation properties of the sixth Painlevé equation and one-parameter families of solutions,

Lett. Nuovo Cimento (2) 30 (17), pp. 539–544.

External Links:

ISSN 0024-1318, MathReview (D. A. Lutz).

Referenced by:

§32.10(vi).

Encodings:

BibTeX
A. S. Fokas, A. R. Its, A. A. Kapaev and V. Yu. Novokshënov (2006)
Painlevé Transcendents: The Riemann-Hilbert Approach,

Mathematical Surveys and Monographs, Vol. 128, American Mathematical Society, Providence, RI.

External Links:

ISBN 0-8218-3651-X, MathReview Entry, ZentralBlatt.

Referenced by:

§32.11(ii), §32.11(iii), §32.11(iv), §32.12(ii), §32.12(iii), §32.4(i), Alexander A. Its.

Encodings:

BibTeX
K. W. Ford and J. A. Wheeler (1959a)
Semiclassical description of scattering,

Ann. Physics 7 (3), pp. 259–286.

External Links:

ISSN 0003-4916, Document, MathReview, ZentralBlatt.

Referenced by:

§9.16.

Encodings:

BibTeX
K. W. Ford and J. A. Wheeler (1959b)
Application of semiclassical scattering analysis,

Ann. Physics 7 (3), pp. 287–322.

External Links:

ISSN 0003-4916, Document, MathReview, ZentralBlatt.

Referenced by:

§9.16.

Encodings:

BibTeX
W. B. Ford (1960)
Studies on Divergent Series and Summability & The Asymptotic Developments of Functions Defined by Maclaurin Series,

Chelsea Publishing Co., New York.

Notes:

Reprint with corrections of two books published originally in 1916 and 1936.

External Links:

MathReview.

Referenced by:

¶ ‣ §2.10(iii).

Encodings:

BibTeX
B. Fornberg and J. A. C. Weideman (2011)
A numerical methodology for the Painlevé equations,

J. Comput. Phys. 230 (15), pp. 5957–5973.

External Links:

ISSN 0021-9991, Document, FullText, MathReview Entry, ZentralBlatt.

Referenced by:

§32.17.

Encodings:

BibTeX
P. J. Forrester and N. S. Witte (2001)
Application of the $\tau$ -function theory of Painlevé equations to random matrices: PIV, PII and the GUE,

Comm. Math. Phys. 219 (2), pp. 357–398.

External Links:

ISSN 0010-3616, Document, MathReview (Alexei Khorunzhy), ZentralBlatt.

Referenced by:

§32.10(iv), §32.14, §32.6(v).

Encodings:

BibTeX
P. J. Forrester and N. S. Witte (2002)
Application of the $\tau$ -function theory of Painlevé equations to random matrices: $\mathrm{P}_{\mathrm{V}}$ , $\mathrm{P}_{\mathrm{III}}$ , the LUE, JUE, and CUE,

Comm. Pure Appl. Math. 55 (6), pp. 679–727.

External Links:

ISSN 0010-3640, Document, MathReview (Mark Adler), ZentralBlatt.

Referenced by:

§32.10(iii), §32.10(v), §32.14, §32.6(iv), §32.6(v).

Encodings:

BibTeX
P. J. Forrester and N. S. Witte (2004)
Application of the $\tau$ -function theory of Painlevé equations to random matrices: $\rm P_{{\rm VI}}$ , the JUE, CyUE, cJUE and scaled limits,

Nagoya Math. J. 174, pp. 29–114.

External Links:

ISSN 0027-7630, MathReview, ZentralBlatt.

Referenced by:

§32.10(vi), §32.6(v).

Encodings:

BibTeX
R. C. Forrey (1997)
Computing the hypergeometric function,

J. Comput. Phys. 137 (1), pp. 79–100.

Notes:

Double-precision Fortran

External Links:

ISSN 0021-9991, Document, Code, MathReview (J. P. Singhal), ZentralBlatt.

Referenced by:

§15.19(i), §15.20(ii), §15.20(iii).

Encodings:

BibTeX
T. Fort (1948)
Finite Differences and Difference Equations in the Real Domain,

Clarendon Press, Oxford.

External Links:

MathReview (W. J. Trjitzinsky), ZentralBlatt.

Referenced by:

¶ ‣ §26.1, ¶ ‣ §26.1.

Encodings:

BibTeX
L. Fox and I. B. Parker (1968)
Chebyshev Polynomials in Numerical Analysis,

Oxford University Press, London.

Notes:

Reprinted in 1972 with corrections.

External Links:

MathReview (G. N. Lance), ZentralBlatt.

Referenced by:

¶ ‣ §3.11(ii).

Encodings:

BibTeX
L. Fox (1960)
Tables of Weber Parabolic Cylinder Functions and Other Functions for Large Arguments,

National Physical Laboratory Mathematical Tables, Vol. 4. Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London.

External Links:

MathReview (L. J. Slater), ZentralBlatt.

Referenced by:

§12.19, §9.18(ii).

Encodings:

BibTeX
P. A. Fox, A. D. Hall and N. L. Schryer (1978)
The PORT mathematical subroutine library,

ACM Trans. Math. Software 4 (2), pp. 104–126.

Notes:

Single- and double-precision Fortran.

External Links:

ISSN 0098-3500, Document.

Referenced by:

§10.77(ii), §10.77(iv).

Encodings:

BibTeX
C. H. Franke (1965)
Numerical evaluation of the elliptic integral of the third kind,

Math. Comp. 19 (91), pp. 494–496.

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

§19.36(iv).

Encodings:

BibTeX
C. K. Frederickson and P. L. Marston (1992)
Transverse cusp diffraction catastrophes produced by the reflection of ultrasonic tone bursts from a curved surface in water,

J. Acoust. Soc. Amer. 92 (5), pp. 2869–2877.

External Links:

Document.

Referenced by:

§36.14(iv).

Encodings:

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C. K. Frederickson and P. L. Marston (1994)
Travel time surface of a transverse cusp caustic produced by reflection of acoustical transients from a curved metal surface,

J. Acoust. Soc. Amer. 95 (2), pp. 650–660.

External Links:

Document.

Referenced by:

§36.14(iv).

Encodings:

BibTeX
C. L. Frenzen and R. Wong (1985)
A note on asymptotic evaluation of some Hankel transforms,

Math. Comp. 45 (172), pp. 537–548.

External Links:

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

Referenced by:

§10.22(v), §18.15(i), §18.16(ii).

Encodings:

BibTeX
C. L. Frenzen and R. Wong (1986)
Asymptotic expansions of the Lebesgue constants for Jacobi series,

Pacific J. Math. 122 (2), pp. 391–415.

External Links:

ISSN 0030-8730, MathReview (Paolo M. Soardi), ZentralBlatt.

Referenced by:

¶ ‣ §1.8(i).

Encodings:

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C. L. Frenzen and R. Wong (1988)
Uniform asymptotic expansions of Laguerre polynomials,

SIAM J. Math. Anal. 19 (5), pp. 1232–1248.

External Links:

ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt.

Referenced by:

§18.15(iv).

Encodings:

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C. L. Frenzen (1990)
Error bounds for a uniform asymptotic expansion of the Legendre function ${Q}^{{-m}}_{n}({\rm cosh}\, z)$ ,

SIAM J. Math. Anal. 21 (2), pp. 523–535.

External Links:

ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt.

Referenced by:

§14.26.

Encodings:

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A. Fresnel (1818)
Mémoire sur la diffraction de la lumière,

Mém. de l’Académie des Sciences, pp. 247–382.

Notes:

Œvres Complètes d’Augustin Fresnel, Paris, 1866

Referenced by:

Figure 7.3.4, Figure 7.3.4.

Encodings:

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G. Freud (1976)
On the coefficients in the recursion formulae of orthogonal polynomials,

Proc. Roy. Irish Acad. Sect. A 76 (1), pp. 1–6.

External Links:

MathReview (A. G. Law), ZentralBlatt.

Referenced by:

§32.15.

Encodings:

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B. D. Fried and S. D. Conte (1961)
The Plasma Dispersion Function: The Hilbert Transform of the Gaussian.,

Academic Press, London-New York.

Notes:

Erratum: Math. Comp. v. 26 (1972), no. 119, p. 814.

External Links:

MathReview (R. Balescu).

Referenced by:

§7.21.

Encodings:

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B. R. Frieden (1971)
Evaluation, design and extrapolation methods for optical signals, based on use of the prolate functions,

in Progress in Optics,

Vol. 9, pp. 311–407.

Referenced by:

§30.15(i), §30.15(ii), §30.15(iii), §30.15(iv), §30.15(v), §30.15(v).

Encodings:

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F. G. Friedlander (1958)
Sound Pulses,

Cambridge University Press, Cambridge-New York.

External Links:

MathReview (A. E. Heins), ZentralBlatt.

Referenced by:

§9.16.

Encodings:

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F. N. Fritsch, R. E. Shafer and W. P. Crowley (1973)
Solution of the transcendental equation $we^{w}=x$ ,

Comm. ACM 16 (2), pp. 123–124.

Notes:

Includes Fortran code.

External Links:

ISSN 0001-0782, Document.

Referenced by:

§4.48(iv).

Encodings:

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C. Fröberg (1955)
Numerical treatment of Coulomb wave functions,

Rev. Mod. Phys. 27 (4), pp. 399–411.

External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

§33.10(ii), §33.11, §33.12(i), §33.9(ii).

Encodings:

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R. Fuchs (1907)
Über lineare homogene Differentialgleichungen zweiter Ordnung mit drei im Endlichen gelegenen wesentlich singulären Stellen,

Math. Ann. 63 (3), pp. 301–321.

External Links:

ISSN 0025-5831, Document, ZentralBlatt.

Referenced by:

§32.2(iv).

Encodings:

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Y. Fukui and T. Horiguchi (1992)
Characteristic values of the integral equation satisfied by the Mathieu functions and its application to a system with chirality-pair interaction on a one-dimensional lattice,

Phys. A 190 (3-4), pp. 346–362.

External Links:

ISSN 0378-4371, Document, MathReview.

Referenced by:

§28.33(iii).

Encodings:

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T. Fukushima (2010)
Fast computation of incomplete elliptic integral of first kind by half argument transformation,

Numer. Math. 116 (4), pp. 687–719.

External Links:

ISSN 0029-599X, Document, FullText, MathReview (Mehdi Hassani), ZentralBlatt.

Referenced by:

§19.36(iv), §19.36(iv).

Encodings:

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T. Fukushima (2012)
Series expansions of symmetric elliptic integrals,

Math. Comp. 81 (278), pp. 957–990.

External Links:

Document.

Referenced by:

§20.7(ii), §20.7(ii).

Encodings:

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L. W. Fullerton and G. A. Rinker (1986)
Generalized Fermi-Dirac integrals—FD, FDG, FDH,

Comput. Phys. Comm. 39 (2), pp. 181–185.

External Links:

ISSN 0010-4655, Document, Code, MathReview.

Referenced by:

§25.21(vii).

Encodings:

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L. W. Fullerton (1972)
Algorithm 435: Modified incomplete gamma function,

Comm. ACM 15 (11), pp. 993–995.

Notes:

Includes Fortran code. For a Remark see ACM Trans. Math. Software 4 (1978), no. 3, pp. 296–304.

External Links:

ISSN 0001-0782, Document, Remark.

Referenced by:

§8.28(ii).

Encodings:

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L. W. Fullerton (1977)
Portable Special Function Routines,

in Portability of Numerical Software (Oak Brook, Illinois, 1976),

Lecture Notes in Computer Science, Vol. 57, pp. 452–483.

External Links:

Package FN (in GAMS).

Referenced by:

FN (free Fortran library).

Encodings:

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Y. V. Fyodorov (2005)
Introduction to the Random Matrix Theory: Gaussian Unitary Ensemble and Beyond,

in Recent Perspectives in Random Matrix Theory and Number Theory,

London Math. Soc. Lecture Note Ser., Vol. 322, pp. 31–78.

External Links:

MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §18.38(ii).

Encodings:

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