Bibliography O

♦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♦

F. Oberhettinger and T. P. Higgins (1961)
Tables of Lebedev, Mehler and Generalized Mehler Transforms,

Mathematical Note

Technical Report 246, Boeing Scientific Research Lab, Seattle.

Referenced by:

§1.14(viii).

Encodings:

BibTeX
F. Oberhettinger (1990)
Tables of Fourier Transforms and Fourier Transforms of Distributions,

Springer-Verlag, Berlin.

External Links:

ISBN 3-540-50630-6; 0-387-50630-6, MathReview, ZentralBlatt.

Referenced by:

§1.14(viii), §10.22(vi), §10.43(vi), §11.10(x), §11.7(v), §11.9(iv), ¶ ‣ §12.12, §13.10(iv), §13.23(ii), §18.17(ix), §6.14(iii), §7.14(iii).

Encodings:

BibTeX
F. Oberhettinger and L. Badii (1973)
Tables of Laplace Transforms,

Springer-Verlag, Berlin-New York.

Notes:

Table errata: Math. Comp. v. 50 (1988), no. 182, pp. 653–654.

External Links:

ISBN 0-387-06350-1, MathReview, ZentralBlatt.

Referenced by:

§1.14(viii), §10.22(vi), §10.43(vi), §11.5(iii), §11.7(v), §11.9(iv), ¶ ‣ §12.12, §12.5(iv), ¶ ‣ §13.10(ii), §13.23(i), §14.17(v), §15.14, §18.17(ix), §20.10(ii), ¶ ‣ §5.13, §6.14(iii), §6.7(iv), §7.14(iii), §7.7(iii), §8.6(iii).

Encodings:

BibTeX
F. Oberhettinger (1972)
Tables of Bessel Transforms,

Springer-Verlag, Berlin-New York.

Notes:

Table errata: Math. Comp. v. 65 (1996), no. 215, p. 1386.

External Links:

ISBN 0-387-05997-0, MathReview, ZentralBlatt.

Referenced by:

§1.14(viii), §10.22(v), §10.43(v), §10.43(vi), §11.10(x), §11.5(iii), §11.7(v), §11.9(iv), §13.10(v), §13.23(iii), §15.14, §18.17(ix), §8.14, §8.6(iii).

Encodings:

BibTeX
F. Oberhettinger (1973)
Fourier Expansions. A Collection of Formulas,

Academic Press, New York-London.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§1.8(v), §22.11, §4.27.

Encodings:

BibTeX
F. Oberhettinger (1974)
Tables of Mellin Transforms,

Springer-Verlag, Berlin-New York.

External Links:

ISBN 0-387-06942-9, MathReview, ZentralBlatt.

Referenced by:

§1.14(viii), §10.22(vi), §10.43(vi), §11.10(x), §11.5(iii), §11.7(v), §11.9(iv), ¶ ‣ §12.12, §12.5(iv), §13.10(iii), §13.23(i), §14.17(vi), §15.14, §18.17(ix), §20.10(i), ¶ ‣ §5.13, §6.14(iii), §6.7(iv), §7.14(iii), §7.7(iii).

Encodings:

BibTeX
A. M. Odlyzko (1987)
On the distribution of spacings between zeros of the zeta function,

Math. Comp. 48 (177), pp. 273–308.

External Links:

ISSN 0025-5718, FullText, Author’s Website, MathReview (S. L. Segal), ZentralBlatt.

Referenced by:

§25.18(ii).

Encodings:

BibTeX
A. M. Odlyzko (1995)
Asymptotic Enumeration Methods,

in Handbook of Combinatorics, Vol. 2,

(R. L. Graham and M. Grötschel Eds.), pp. 1063–1229.

External Links:

ISBN 0-444-82351-4, Pdf, MathReview (Konrad Engel), ZentralBlatt.

Referenced by:

Ch.2.

Encodings:

BibTeX
O. M. Ogreid and P. Osland (1998)
Summing one- and two-dimensional series related to the Euler series,

J. Comput. Appl. Math. 98 (2), pp. 245–271.

External Links:

ISSN 0377-0427, Document, MathReview (Boris Petrovich Osilenker), ZentralBlatt.

Referenced by:

§25.8.

Encodings:

BibTeX
K. Okamoto (1981)
On the $\tau$ -function of the Painlevé equations,

Phys. D 2 (3), pp. 525–535.

External Links:

ISSN 0167-2789, Document, MathReview (D. A. Lutz).

Referenced by:

§32.6(i), §32.6(ii).

Encodings:

BibTeX
K. Okamoto (1986)
Studies on the Painlevé equations. III. Second and fourth Painlevé equations, $P_{{{\rm II}}}$ and $P_{{\mathrm{IV}}}$ ,

Math. Ann. 275 (2), pp. 221–255.

External Links:

ISSN 0025-5831, Document, MathReview (Hélène Airault), ZentralBlatt.

Referenced by:

§32.10(ii), §32.10(iv), §32.6(iii), §32.6(v), §32.7(viii).

Encodings:

BibTeX
K. Okamoto (1987a)
Studies on the Painlevé equations. I. Sixth Painlevé equation $P_{{{\rm VI}}}$ ,

Ann. Mat. Pura Appl. (4) 146, pp. 337–381.

External Links:

ISSN 0003-4622, Document, MathReview (Hélène Airault), ZentralBlatt.

Referenced by:

§32.10(vi), §32.6(v), §32.7(vii), §32.7(viii).

Encodings:

BibTeX
K. Okamoto (1987b)
Studies on the Painlevé equations. II. Fifth Painlevé equation $P_{{\rm V}}$ ,

Japan. J. Math. (N.S.) 13 (1), pp. 47–76.

External Links:

ISSN 0289-2316, MathReview (Hélène Airault), ZentralBlatt.

Referenced by:

§32.10(v), §32.6(v), §32.7(viii).

Encodings:

BibTeX
K. Okamoto (1987c)
Studies on the Painlevé equations. IV. Third Painlevé equation $P_{{{\rm III}}}$ ,

Funkcial. Ekvac. 30 (2-3), pp. 305–332.

External Links:

ISSN 0532-8721, FullText, MathReview (Hélène Airault), ZentralBlatt.

Referenced by:

§32.10(iii), §32.2(iii), §32.6(iv), §32.7(viii).

Encodings:

BibTeX
S. Okui (1974)
Complete elliptic integrals resulting from infinite integrals of Bessel functions,

J. Res. Nat. Bur. Standards Sect. B 78B (3), pp. 113–135.

External Links:

ISSN 0160-1741, MathReview (Y. L. Luke), ZentralBlatt.

Referenced by:

§10.22(vi), §10.43(vi).

Encodings:

BibTeX
S. Okui (1975)
Complete elliptic integrals resulting from infinite integrals of Bessel functions. II,

J. Res. Nat. Bur. Standards Sect. B 79B (3-4), pp. 137–170.

External Links:

ISSN 0160-1741, MathReview (Y. L. Luke), ZentralBlatt.

Referenced by:

§10.22(vi), §10.43(vi).

Encodings:

BibTeX
A. B. Olde Daalhuis and F. W. J. Olver (1994)
Exponentially improved asymptotic solutions of ordinary differential equations. II Irregular singularities of rank one,

Proc. Roy. Soc. London Ser. A 445, pp. 39–56.

External Links:

ISSN 0962-8444, FullText, MathReview (Hussain S. Nur), ZentralBlatt.

Referenced by:

§13.4(i), §2.11(v), §2.7(ii).

Encodings:

BibTeX
A. B. Olde Daalhuis and F. W. J. Olver (1995a)
Hyperasymptotic solutions of second-order linear differential equations. I,

Methods Appl. Anal. 2 (2), pp. 173–197.

External Links:

ISSN 1073-2772, FullText, MathReview (A. D. Wood), ZentralBlatt.

Referenced by:

§10.17(v), §10.40(iv), §13.29(i), §13.7(iii), §2.11(v), §9.7(v).

Encodings:

BibTeX
A. B. Olde Daalhuis and F. W. J. Olver (1995b)
On the calculation of Stokes multipliers for linear differential equations of the second order,

Methods Appl. Anal. 2 (3), pp. 348–367.

External Links:

ISSN 1073-2772, Pdf, MathReview (Archibald D. MacGillivray), ZentralBlatt.

Referenced by:

§2.7(ii).

Encodings:

BibTeX
A. B. Olde Daalhuis and F. W. J. Olver (1998)
On the asymptotic and numerical solution of linear ordinary differential equations,

SIAM Rev. 40 (3), pp. 463–495.

External Links:

ISSN 1095-7200, Document, MathReview (W. Balser), ZentralBlatt.

Referenced by:

§16.25, §2.7(ii), §3.7(iii).

Encodings:

BibTeX
A. B. Olde Daalhuis and N. M. Temme (1994)
Uniform Airy-type expansions of integrals,

SIAM J. Math. Anal. 25 (2), pp. 304–321.

External Links:

ISSN 0036-1410, Document, MathReview, ZentralBlatt.

Referenced by:

§2.4(v).

Encodings:

BibTeX
A. B. Olde Daalhuis (1994)
Asymptotic expansions for $q$ -gamma, $q$ -exponential, and $q$ -Bessel functions,

J. Math. Anal. Appl. 186 (3), pp. 896–913.

External Links:

ISSN 0022-247X, Document, MathReview (P. K. Banerji), ZentralBlatt.

Referenced by:

§5.18(ii).

Encodings:

BibTeX
A. B. Olde Daalhuis (1995)
Hyperasymptotic solutions of second-order linear differential equations. II,

Methods Appl. Anal. 2 (2), pp. 198–211.

External Links:

ISSN 1073-2772, FullText, MathReview (A. D. Wood), ZentralBlatt.

Referenced by:

§10.17(v), §10.40(iv), §2.11(v), §9.7(v).

Encodings:

BibTeX
A. B. Olde Daalhuis (1996)
Hyperterminants. I,

J. Comput. Appl. Math. 76 (1-2), pp. 255–264.

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt.

Referenced by:

§10.17(v), §10.40(iv), §2.11(v), §9.7(v).

Encodings:

BibTeX
A. B. Olde Daalhuis (1998a)
Hyperasymptotic solutions of higher order linear differential equations with a singularity of rank one,

Proc. Roy. Soc. London Ser. A 454, pp. 1–29.

External Links:

ISSN 1364-5021, Document, MathReview (Donald A. Lutz), ZentralBlatt.

Referenced by:

§2.11(v), §2.7(ii).

Encodings:

BibTeX
A. B. Olde Daalhuis (1998b)
Hyperterminants. II,

J. Comput. Appl. Math. 89 (1), pp. 87–95.

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt.

Referenced by:

§2.11(v).

Encodings:

BibTeX
A. B. Olde Daalhuis (1998c)
On the resurgence properties of the uniform asymptotic expansion of the incomplete gamma function,

Methods Appl. Anal. 5 (4), pp. 425–438.

External Links:

ISSN 1073-2772, Pdf, MathReview (Éric Delabaere), ZentralBlatt.

Referenced by:

§8.12.

Encodings:

BibTeX
A. B. Olde Daalhuis (2000)
On the asymptotics for late coefficients in uniform asymptotic expansions of integrals with coalescing saddles,

Methods Appl. Anal. 7 (4), pp. 727–745.

External Links:

ISSN 1073-2772, Pdf, MathReview (Raimundas Vidunas), ZentralBlatt.

Referenced by:

§36.12(iii).

Encodings:

BibTeX
A. B. Olde Daalhuis (2003a)
Uniform asymptotic expansions for hypergeometric functions with large parameters. I,

Analysis and Applications (Singapore) 1 (1), pp. 111–120.

External Links:

ISSN 0219-5305, Document, MathReview, ZentralBlatt.

Referenced by:

§15.12(iii).

Encodings:

BibTeX
A. B. Olde Daalhuis (2003b)
Uniform asymptotic expansions for hypergeometric functions with large parameters. II,

Analysis and Applications (Singapore) 1 (1), pp. 121–128.

External Links:

ISSN 0219-5305, Document, MathReview, ZentralBlatt.

Referenced by:

§15.12(iii).

Encodings:

BibTeX
A. B. Olde Daalhuis (2004a)
Inverse factorial-series solutions of difference equations,

Proc. Edinb. Math. Soc. (2) 47 (2), pp. 421–448.

External Links:

ISSN 0013-0915, Document, MathReview (Niro Yanagihara), ZentralBlatt.

Referenced by:

§2.9(i).

Encodings:

BibTeX
A. B. Olde Daalhuis (2004b)
On higher-order Stokes phenomena of an inhomogeneous linear ordinary differential equation,

J. Comput. Appl. Math. 169 (1), pp. 235–246.

External Links:

ISSN 0377-0427, Document, MathReview (Jorge Mozo Fernández), ZentralBlatt.

Referenced by:

§2.11(iv).

Encodings:

BibTeX
A. B. Olde Daalhuis (2005a)
Hyperasymptotics for nonlinear ODEs. I. A Riccati equation,

Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2060), pp. 2503–2520.

External Links:

ISSN 1364-5021, Document, MathReview, ZentralBlatt.

Referenced by:

§2.11(v).

Encodings:

BibTeX
A. B. Olde Daalhuis (2005b)
Hyperasymptotics for nonlinear ODEs. II. The first Painlevé equation and a second-order Riccati equation,

Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2062), pp. 3005–3021.

External Links:

ISSN 1364-5021, Document, MathReview, ZentralBlatt.

Referenced by:

§2.11(v), §32.12(i).

Encodings:

BibTeX
A. B. Olde Daalhuis (2010)
Uniform asymptotic expansions for hypergeometric functions with large parameters. III,

Analysis and Applications (Singapore).

Notes:

In press.

External Links:

ISSN 0219-5305.

Referenced by:

§15.12(iii).

Encodings:

BibTeX
M. N. Olevskiĭ (1950)
Triorthogonal systems in spaces of constant curvature in which the equation $\Delta _{{2}}u+\lambda u=0$ allows a complete separation of variables,

Mat. Sbornik N.S. 27(69) (3), pp. 379–426 (Russian).

Notes:

In Russian.

External Links:

MathReview (H. Busemann), ZentralBlatt.

Referenced by:

§31.17(i).

Encodings:

BibTeX
T. Oliveira e Silva (2006)
Computing $\pi(x)$ : The combinatorial method,

Revista do DETUA 4 (6), pp. 759–768.

Notes:

Online fulltext contains postpublication annotations.

External Links:

FullText.

Referenced by:

§27.18.

Encodings:

BibTeX
J. Oliver (1977)
An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series,

J. Inst. Math. Appl. 20 (3), pp. 379–391.

External Links:

Document, MathReview (David L. Elliott), ZentralBlatt.

Referenced by:

¶ ‣ §3.11(ii).

Encodings:

BibTeX
I. Olkin (1959)
A class of integral identities with matrix argument,

Duke Math. J. 26 (2), pp. 207–213.

External Links:

Document, MathReview (R. Bellman), ZentralBlatt.

Referenced by:

§35.3(ii).

Encodings:

BibTeX
F. W. J. Olver and J. M. Smith (1983)
Associated Legendre functions on the cut,

J. Comput. Phys. 51 (3), pp. 502–518.

Notes:

Includes single, double precision Fortran code.

External Links:

SLATEC module DXNRMP (in GAMS), ISSN 0021-9991, Document, MathReview (G. P. Bhattacharjee), ZentralBlatt.

Referenced by:

§14.32, §14.34(ii).

Encodings:

BibTeX
F. W. J. Olver and D. J. Sookne (1972)
Note on backward recurrence algorithms,

Math. Comp. 26 (120), pp. 941–947.

External Links:

FullText, MathReview (Walter Gautschi), ZentralBlatt.

Referenced by:

§10.74(iv), §3.6(v).

Encodings:

BibTeX
F. W. J. Olver and F. Stenger (1965)
Error bounds for asymptotic solutions of second-order differential equations having an irregular singularity of arbitrary rank,

J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (2), pp. 244–249.

External Links:

Document, MathReview, ZentralBlatt.

Referenced by:

§2.7(ii).

Encodings:

BibTeX
F. W. J. Olver (1950)
A new method for the evaluation of zeros of Bessel functions and of other solutions of second-order differential equations,

Proc. Cambridge Philos. Soc. 46 (4), pp. 570–580.

External Links:

Document, MathReview (J. Todd), ZentralBlatt.

Referenced by:

§10.21(ii).

Encodings:

BibTeX
F. W. J. Olver (1951)
A further method for the evaluation of zeros of Bessel functions and some new asymptotic expansions for zeros of functions of large order,

Proc. Cambridge Philos. Soc. 47, pp. 699–712.

External Links:

Document, MathReview (J. Todd), ZentralBlatt.

Referenced by:

§10.21(vii).

Encodings:

BibTeX

F. W. J. Olver (1952)
Some new asymptotic expansions for Bessel functions of large orders,

Proc. Cambridge Philos. Soc. 48 (3), pp. 414–427.

External Links:

Document, MathReview (F. Oberhettinger), ZentralBlatt.

Referenced by:

§10.19(iii), §10.21(vii).

Encodings:

BibTeX
F. W. J. Olver (1954)
The asymptotic expansion of Bessel functions of large order,

Philos. Trans. Roy. Soc. London. Ser. A. 247, pp. 328–368.

External Links:

FullText, MathReview (N. D. Kazarinoff), ZentralBlatt.

Referenced by:

§10.20(ii), §10.20(ii), §10.21(viii), §10.21(ix), ¶ ‣ §10.75(iii), §9.9(iii), §9.9(iv).

Encodings:

BibTeX
F. W. J. Olver (1959)
Uniform asymptotic expansions for Weber parabolic cylinder functions of large orders,

J. Res. Nat. Bur. Standards Sect. B 63B, pp. 131–169.

External Links:

MathReview (N. D. Kazarinoff), ZentralBlatt.

Referenced by:

§12.10(i), §12.10(ii), §12.10(iii), §12.10(iv), §12.10(v), §12.10(vii), §12.10(vii), §12.11(iii), §12.11(iii), ¶ ‣ §12.14(ix), §12.14(xi), §12.14(ix), §12.14(ix), Ch.12, §18.16(v).

Encodings:

BibTeX
F. W. J. Olver (Ed.) (1960)
Bessel Functions. Part III: Zeros and Associated Values,

Royal Society Mathematical Tables, Volume 7, Cambridge University Press, Cambridge-New York.

External Links:

ISBN 0-521-06153-9, MathReview (L. Fox), ZentralBlatt.

Referenced by:

§10.21(vi), §10.21(viii), §10.58, ¶ ‣ §10.74(vi), §10.75(x), ¶ ‣ §10.75(iii).

Encodings:

BibTeX
F. W. J. Olver (1962)
Tables for Bessel Functions of Moderate or Large Orders,

National Physical Laboratory Mathematical Tables, Vol. 6. Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London.

External Links:

MathReview (I. A. Stegun), ZentralBlatt.

Referenced by:

¶ ‣ §10.20(i), §10.41(ii), §10.75(ii), §10.75(v).

Encodings:

BibTeX
F. W. J. Olver (1964a)
Error analysis of Miller’s recurrence algorithm,

Math. Comp. 18 (85), pp. 65–74.

External Links:

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

Referenced by:

§3.6(iii).

Encodings:

BibTeX
F. W. J. Olver (1964b)
Error bounds for asymptotic expansions in turning-point problems,

J. Soc. Indust. Appl. Math. 12 (1), pp. 200–214.

External Links:

Document, MathReview (N. D. Kazarinoff), ZentralBlatt.

Referenced by:

§2.8(iii).

Encodings:

BibTeX
F. W. J. Olver (1965)
On the asymptotic solution of second-order differential equations having an irregular singularity of rank one, with an application to Whittaker functions,

J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (2), pp. 225–243.

External Links:

Document, MathReview (T. E. Hull), ZentralBlatt.

Referenced by:

§13.19, §13.7(ii).

Encodings:

BibTeX
F. W. J. Olver (1967a)
Numerical solution of second-order linear difference equations,

J. Res. Nat. Bur. Standards Sect. B 71B, pp. 111–129.

External Links:

MathReview (G. N. Lance), ZentralBlatt.

Referenced by:

§3.6(iv), §3.6(v).

Encodings:

BibTeX
F. W. J. Olver (1967b)
Bounds for the solutions of second-order linear difference equations,

J. Res. Nat. Bur. Standards Sect. B 71B (4), pp. 161–166.

External Links:

MathReview (C. W. Clenshaw), ZentralBlatt.

Referenced by:

§2.9(i).

Encodings:

BibTeX
F. W. J. Olver (1970)
A paradox in asymptotics,

SIAM J. Math. Anal. 1 (4), pp. 533–534.

External Links:

Document, MathReview (L. Hoischen), ZentralBlatt.

Referenced by:

¶ ‣ §2.10(iv).

Encodings:

BibTeX
F. W. J. Olver (1974)
Error bounds for stationary phase approximations,

SIAM J. Math. Anal. 5 (1), pp. 19–29.

Notes:

See also Olver (1997b)

External Links:

Document, MathReview (L. Berg), ZentralBlatt.

Referenced by:

§2.3(iv).

Encodings:

BibTeX
F. W. J. Olver (1975a)
Second-order linear differential equations with two turning points,

Philos. Trans. Roy. Soc. London Ser. A 278, pp. 137–174.

External Links:

FullText, MathReview (P. F. Hsieh), ZentralBlatt.

Referenced by:

§2.8(vi).

Encodings:

BibTeX
F. W. J. Olver (1975b)
Legendre functions with both parameters large,

Philos. Trans. Roy. Soc. London Ser. A 278, pp. 175–185.

External Links:

FullText, MathReview (P. F. Hsieh), ZentralBlatt.

Referenced by:

§14.15(v), §14.15(v).

Encodings:

BibTeX
F. W. J. Olver (1976)
Improved error bounds for second-order differential equations with two turning points,

J. Res. Nat. Bur. Standards Sect. B 80B (4), pp. 437–440.

External Links:

MathReview (Peter Deuflhard), ZentralBlatt.

Referenced by:

§2.8(vi).

Encodings:

BibTeX
F. W. J. Olver (1977a)
Connection formulas for second-order differential equations with multiple turning points,

SIAM J. Math. Anal. 8 (1), pp. 127–154.

External Links:

Document, MathReview (Anthony Leung), ZentralBlatt.

Referenced by:

§2.8(v), §9.13(i), §9.13(i).

Encodings:

BibTeX
F. W. J. Olver (1977b)
Connection formulas for second-order differential equations having an arbitrary number of turning points of arbitrary multiplicities,

SIAM J. Math. Anal. 8 (4), pp. 673–700.

External Links:

Document, MathReview (W. Wasow), ZentralBlatt.

Referenced by:

§2.8(v).

Encodings:

BibTeX
F. W. J. Olver (1977c)
Second-order differential equations with fractional transition points,

Trans. Amer. Math. Soc. 226, pp. 227–241.

External Links:

FullText, MathReview (Anthony Leung), ZentralBlatt.

Referenced by:

§2.8(v).

Encodings:

BibTeX
F. W. J. Olver (1978)
General connection formulae for Liouville-Green approximations in the complex plane,

Philos. Trans. Roy. Soc. London Ser. A 289, pp. 501–548.

External Links:

ISSN 0080-4614, FullText, MathReview (W. Wasow), ZentralBlatt.

Referenced by:

§2.8(v), §9.13(i), §9.13(i).

Encodings:

BibTeX
F. W. J. Olver (1980a)
Asymptotic approximations and error bounds,

SIAM Rev. 22 (2), pp. 188–203.

External Links:

ISSN 0036-1445, Document, MathReview (L. Berg), ZentralBlatt.

Referenced by:

¶ ‣ §2.7(iii).

Encodings:

BibTeX
F. W. J. Olver (1980b)
Whittaker functions with both parameters large: Uniform approximations in terms of parabolic cylinder functions,

Proc. Roy. Soc. Edinburgh Sect. A 86 (3-4), pp. 213–234.

External Links:

ISSN 0308-2105, MathReview (P. F. Hsieh), ZentralBlatt.

Referenced by:

§13.20(iii), §13.20(iv).

Encodings:

BibTeX
F. W. J. Olver (1983)
Error Analysis of Complex Arithmetic,

in Computational Aspects of Complex Analysis (Braunlage, 1982),

(L. Wuytack, E. Ng and H. J. Bünger Eds.), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., Vol. 102, pp. 279–292.

External Links:

MathReview (G. Blanch), ZentralBlatt.

Referenced by:

§3.1(v).

Encodings:

BibTeX
F. W. J. Olver (1991a)
Uniform, exponentially improved, asymptotic expansions for the generalized exponential integral,

SIAM J. Math. Anal. 22 (5), pp. 1460–1474.

External Links:

ISSN 0036-1410, Document, MathReview (Hans-Jürgen Glaeske), ZentralBlatt.

Referenced by:

§2.11(iii), §2.11(iii), §8.11(i), §8.20(i).

Encodings:

BibTeX
F. W. J. Olver (1991b)
Uniform, exponentially improved, asymptotic expansions for the confluent hypergeometric function and other integral transforms,

SIAM J. Math. Anal. 22 (5), pp. 1475–1489.

External Links:

ISSN 0036-1410, Document, MathReview (Hans-Jürgen Glaeske), ZentralBlatt.

Referenced by:

§10.17(v), §10.40(iv), §13.7(iii), §9.7(v).

Encodings:

BibTeX
F. W. J. Olver (1993a)
Exponentially-improved asymptotic solutions of ordinary differential equations I: The confluent hypergeometric function,

SIAM J. Math. Anal. 24 (3), pp. 756–767.

External Links:

ISSN 0036-1410, Document, MathReview (Hussain S. Nur), ZentralBlatt.

Referenced by:

§10.17(v), §13.7(iii), §9.7(v).

Encodings:

BibTeX
F. W. J. Olver (1994a)
Asymptotic expansions of the coefficients in asymptotic series solutions of linear differential equations,

Methods Appl. Anal. 1 (1), pp. 1–13.

External Links:

ISSN 1073-2772, Pdf, MathReview (Archibald D. MacGillivray), ZentralBlatt.

Referenced by:

§2.7(ii), §2.7(ii).

Encodings:

BibTeX
F. W. J. Olver (1994b)
The Generalized Exponential Integral,

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

International Series of Numerical Mathematics, Vol. 119, pp. 497–510.

External Links:

MathReview (Richard B. Paris), ZentralBlatt.

Referenced by:

§2.11(iii), §8.19(viii).

Encodings:

BibTeX
F. W. J. Olver (1995)
On an asymptotic expansion of a ratio of gamma functions,

Proc. Roy. Irish Acad. Sect. A 95 (1), pp. 5–9.

External Links:

ISSN 0035-8975, MathReview (Richard B. Paris), ZentralBlatt.

Referenced by:

§5.11(iii).

Encodings:

BibTeX
F. W. J. Olver (1997a)
Asymptotic solutions of linear ordinary differential equations at an irregular singularity of rank unity,

Methods Appl. Anal. 4 (4), pp. 375–403.

External Links:

ISSN 1073-2772, MathReview (A. D. Wood), ZentralBlatt.

Referenced by:

§2.7(ii).

Encodings:

BibTeX
F. W. J. Olver (1997b)
Asymptotics and Special Functions,

A. K. Peters, Wellesley, MA.

Notes:

Reprint, with corrections, of original Academic Press edition, 1974

External Links:

ISBN 1-56881-069-5, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §1.10(iv), §1.13(i), §1.13(ii), §1.13(iv), §1.17(i), ¶ ‣ §1.4(v), §1.4(ii), §1.4(v), §1.8(i), §1.9(vi), §10.12, §10.14, §10.15, §10.16, §10.17(i), §10.17(iii), §10.17(iv), §10.19(ii), §10.2(ii), §10.20(i), §10.20(ii), §10.20(ii), §10.21(i), §10.21(vi), §10.25(ii), §10.27, §10.31, §10.34, §10.37, §10.4, §10.40(i), §10.40(ii), §10.40(iii), §10.40(iii), §10.41(ii), §10.41(iii), §10.41(iv), §10.41(v), §10.42, §10.6(i), §10.8, §10.9(i), §10.9(iii), Ch.10, §11.10(i), §11.11(iii), §11.11(iii), §11.2(i), §11.2(ii), §11.2(iii), §11.6(i), §11.9(iii), Ch.11, §12.10(vi), §12.2(i), Ch.12, §13.1, §13.14(i), §13.14(ii), §13.14(v), §13.2(i), §13.2(v), §13.20(i), §13.20(ii), §13.20(v), §13.21(i), §13.21(iv), §13.22, §13.7(i), §13.8(i), Ch.13, §14.1, §14.12(ii), §14.15(iii), §14.15(iii), §14.15(iii), §14.16(ii), §14.17(iii), §14.18(ii), §14.2(i), §14.2(ii), §14.2(iii), §14.2(iv), §14.20(vii), §14.20(vii), §14.21(i), §14.21(ii), §14.21(iii), §14.23, §14.24, §14.25, §14.25, §14.26, §14.28(ii), ¶ ‣ §14.3(ii), §14.3(i), §14.3(ii), §14.3(iii), §14.3(iv), §14.7(i), §14.7(ii), §14.7(iv), §14.8(i), §14.8(iii), §14.9(i), §14.9(ii), §14.9(iii), §14.9(iv), Ch.14, §15.1, §15.10(i), §15.11(i), §15.11(ii), §15.12(iii), §15.2(ii), §15.8(i), Ch.15, §16.2(v), §18.15(iii), §18.15(v), §18.16(v), §2.1(i), §2.1(ii), §2.1(iii), §2.1(iii), §2.1(v), ¶ ‣ §2.10(ii), ¶ ‣ §2.10(iii), ¶ ‣ §2.10(iv), §2.10(i), §2.10(ii), §2.10(iii), §2.10(iv), §2.10(iv), §2.11(i), §2.11(i), §2.11(vi), §2.11(vi), ¶ ‣ §2.2, §2.2, §2.3(i), §2.3(ii), §2.3(iii), §2.3(iii), §2.3(v), §2.4(i), §2.4(i), §2.4(ii), §2.4(ii), §2.4(iii), §2.4(iii), §2.4(iv), §2.4(iv), §2.4(v), §2.4(vi), ¶ ‣ §2.7(iii), §2.7(i), §2.7(i), §2.7(ii), §2.7(ii), §2.7(iii), §2.7(iv), §2.8(i), §2.8(ii), §2.8(ii), §2.8(iii), §2.8(iii), §2.8(iv), §2.8(iv), Ch.2, §24.12(i), ¶ ‣ §24.17(i), §24.9, §26.7(iv), §3.9(vi), §4.13, ¶ ‣ §5.11(i), §5.11(i), §5.11(ii), §5.11(iii), §5.12, §5.17, §5.2(i), §5.2(ii), §5.4(i), §5.4(ii), §5.5(i), §5.5(ii), §5.5(iii), §5.7(ii), §5.8, §5.9(i), §5.9(ii), Ch.5, §6.12(i), §6.12(i), §6.2(i), §6.2(ii), §6.4, §6.5, §6.6, Ch.6, §7.12(i), §7.12(iii), §7.2(i), §7.2(ii), §7.2(iii), §7.20(i), §7.5, Ch.7, §8.10, §8.11(i), §8.11(i), §8.2(i), §8.2(ii), Ch.8, §9.10(iv), §9.10(vi), §9.10(viii), §9.12(i), §9.12(iii), §9.12(viii), §9.2(i), §9.2(ii), §9.2(iii), §9.2(iv), §9.2(v), §9.4, §9.5(i), §9.5(ii), §9.6(i), §9.6(ii), §9.7(i), §9.7(ii), §9.7(iii), §9.7(iv), §9.8(i), §9.8(ii), §9.8(iii), §9.9(i), §9.9(ii), Ch.9, Frank W. J. Olver, F. W. J. Olver (1974).

Encodings:

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F. W. J. Olver (1999)
On the uniqueness of asymptotic solutions of linear differential equations,

Methods Appl. Anal. 6 (2), pp. 165–174.

External Links:

ISSN 1073-2772, FullText, MathReview (P. K. Palamides), ZentralBlatt.

Referenced by:

§2.7(ii).

Encodings:

BibTeX
P. J. Olver (1993b)
Applications of Lie Groups to Differential Equations,

2nd edition, Graduate Texts in Mathematics, Vol. 107, Springer-Verlag, New York.

External Links:

ISBN 0-387-94007-3; 0-387-95000-1, MathReview, ZentralBlatt.

Referenced by:

§32.13(i).

Encodings:

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S. Olver (2011)
Numerical solution of Riemann-Hilbert problems: Painlevé II,

Found. Comput. Math. 11 (2), pp. 153–179.

External Links:

ISSN 1615-3375, Document, FullText, MathReview Entry, ZentralBlatt.

Referenced by:

§32.17, §32.17.

Encodings:

BibTeX
On-Line Encyclopedia of Integer Sequences (Web Site)
AT&T Labs, Inc.–Research, Florham Park and Middletown, New Jersey..

Notes:

A tool for finding and identifying integer sequences.

External Links:

On-Line Encyclopedia of Integer Sequences.

Referenced by:

§26.22.

Encodings:

BibTeX
M. K. Ong (1986)
A closed form solution of the $s$ -wave Bethe-Goldstone equation with an infinite repulsive core,

J. Math. Phys. 27 (4), pp. 1154–1158.

External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt.

Referenced by:

§30.13(v).

Encodings:

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K. Ono (2000)
Distribution of the partition function modulo $m$ ,

Ann. of Math. (2) 151 (1), pp. 293–307.

External Links:

ISSN 0003-486X, FullText, MathReview (Bruce C. Berndt), ZentralBlatt.

Referenced by:

§27.14(v).

Encodings:

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G. E. Ordóñez and D. J. Driebe (1996)
Spectral decomposition of tent maps using symmetry considerations,

J. Statist. Phys. 84 (1-2), pp. 269–276.

External Links:

ISSN 0022-4715, Document, MathReview (Makoto Mori), ZentralBlatt.

Referenced by:

§24.18.

Encodings:

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J. M. Ortega and W. C. Rheinboldt (1970)
Iterative Solution of Nonlinear Equations in Several Variables,

Academic Press, New York.

Notes:

Reprinted in 2000 by the Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pennsylvania

External Links:

MathReview (J. F. Traub), ZentralBlatt (Nelli Dimitrova (Sofia)).

Referenced by:

§3.8(vii).

Encodings:

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H. Oser (1960)
Algorithm 22: Riccati-Bessel functions of first and second kind,

Comm. ACM 3 (11), pp. 600–601.

Notes:

Includes Algol code, minimum accuracy 9S. For certification see same journal 13(1970), p. 448.

External Links:

ISSN 0001-0782, Document.

Referenced by:

§10.77(ii).

Encodings:

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A. M. Ostrowski (1973)
Solution of Equations in Euclidean and Banach Spaces,

Pure and Applied Mathematics, Vol. 9, Academic Press, New York-London.

Notes:

Third edition of Solution of equations and systems of equations

External Links:

MathReview (J. Burlak), ZentralBlatt.

Referenced by:

§3.3(v), ¶ ‣ §3.8(iii).

Encodings:

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C. Osácar, J. Palacián and M. Palacios (1995)
Numerical evaluation of the dilogarithm of complex argument,

Celestial Mech. Dynam. Astronom. 62 (1), pp. 93–98.

External Links:

ISSN 0923-2958, Document, MathReview (Bruce C. Berndt), ZentralBlatt.

Referenced by:

§25.18(i).

Encodings:

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R. H. Ott (1985)
Scattering by a parabolic cylinder—a uniform asymptotic expansion,

J. Math. Phys. 26 (4), pp. 854–860.

External Links:

ISSN 0022-2488, Document, MathReview (Jean-Louis Guiraud).

Referenced by:

§12.17.

Encodings:

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M. L. Overton (2001)
Numerical Computing with IEEE Floating Point Arithmetic,

Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

Notes:

Including one theorem, one rule of thumb, and one hundred and one exercises

External Links:

ISBN 0-89871-482-6, MathReview (Jesse L. Barlow), ZentralBlatt.

Referenced by:

¶ ‣ §3.1(i).

Encodings:

BibTeX