hyperasymptotic expansions

(0.002 seconds)

9 matching pages

1: 10.74 Methods of Computation

… ►Furthermore, the attainable accuracy can be increased substantially by use of the exponentially-improved expansions given in §10.17(v), even more so by application of the hyperasymptotic expansions to be found in the references in that subsection. … ► …

2: 2.11 Remainder Terms; Stokes Phenomenon

… ►For other examples see Boyd (1990b), Paris (1992a, b), and Wong and Zhao (2002b). … ►In this way we arrive at hyperasymptotic expansions. …

3: 13.29 Methods of Computation

… ►However, this accuracy can be increased considerably by use of the exponentially-improved forms of expansion supplied by the combination of (13.7.10) and (13.7.11), or by use of the hyperasymptotic expansions given in Olde Daalhuis and Olver (1995a). …

4: 13.7 Asymptotic Expansions for Large Argument

… ►For extensions to hyperasymptotic expansions see Olde Daalhuis and Olver (1995a).

5: Bibliography P

… ►

R. B. Paris (2001a) On the use of Hadamard expansions in hyperasymptotic evaluation. I. Real variables. Proc. Roy. Soc. London Ser. A 457 (2016), pp. 2835–2853.

ⓘ

External Links:: ISSN 1364-5021, Document, MathReview (Andrea Laforgia), ZentralBlatt
Referenced by:: §10.40(iv), §2.11(v).
Encodings:: BibTeX

►

R. B. Paris (2001b) On the use of Hadamard expansions in hyperasymptotic evaluation. II. Complex variables. Proc. Roy. Soc. London Ser. A 457, pp. 2855–2869.

ⓘ

External Links:: ISSN 1364-5021, Document, MathReview (Andrea Laforgia), ZentralBlatt
Referenced by:: §10.40(iv), §2.11(v).
Encodings:: BibTeX

…

6: Bibliography O

… ►

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 (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 (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 (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

…

7: Bibliography H

… ►

P. I. Hadži (1976a) Expansions for the probability function in series of Čebyšev polynomials and Bessel functions. Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 77–80, 96 (Russian).

ⓘ

External Links:: MathReview (V. L. Makarov)
Referenced by:: §7.14(iii).
Encodings:: BibTeX

… ►

R. A. Handelsman and J. S. Lew (1970) Asymptotic expansion of Laplace transforms near the origin. SIAM J. Math. Anal. 1 (1), pp. 118–130.

ⓘ

External Links:: Document, MathReview (E. Riekstiņš), ZentralBlatt
Referenced by:: §2.5(iii), §2.5(ii).
Encodings:: BibTeX

►

R. A. Handelsman and J. S. Lew (1971) Asymptotic expansion of a class of integral transforms with algebraically dominated kernels. J. Math. Anal. Appl. 35 (2), pp. 405–433.

ⓘ

External Links:: Document, MathReview (E. L. Koh), ZentralBlatt
Referenced by:: §2.5(ii).
Encodings:: BibTeX

… ►

F. E. Harris (2000) Spherical Bessel expansions of sine, cosine, and exponential integrals. Appl. Numer. Math. 34 (1), pp. 95–98.

ⓘ

External Links:: ISSN 0168-9274, Document, MathReview, ZentralBlatt
Referenced by:: §10.60(iii), §6.10(ii), §6.15.
Encodings:: BibTeX

… ►

C. J. Howls (1992) Hyperasymptotics for integrals with finite endpoints. Proc. Roy. Soc. London Ser. A 439, pp. 373–396.

ⓘ

External Links:: ISSN 0962-8444, FullText, MathReview, ZentralBlatt
Referenced by:: §2.11(v).
Encodings:: BibTeX

…

8: Bibliography B

… ►

C. B. Balogh (1967) Asymptotic expansions of the modified Bessel function of the third kind of imaginary order. SIAM J. Appl. Math. 15, pp. 1315–1323.

ⓘ

External Links:: ISSN 0036-1399, Document, MathReview (F. W. J. Olver), ZentralBlatt
Referenced by:: §10.45.
Encodings:: BibTeX

… ►

B. C. Berndt and R. J. Evans (1984) Chapter 13 of Ramanujan’s second notebook: Integrals and asymptotic expansions. Expo. Math. 2 (4), pp. 289–347.

ⓘ

External Links:: ISSN 0723-0869, MathReview (F. W. J. Olver), ZentralBlatt
Referenced by:: §2.10(iii).
Encodings:: BibTeX

… ►

M. V. Berry and C. J. Howls (1991) Hyperasymptotics for integrals with saddles. Proc. Roy. Soc. London Ser. A 434, pp. 657–675.

ⓘ

External Links:: ISSN 0962-8444, FullText, MathReview (Andreas Guthmann), ZentralBlatt
Referenced by:: §2.11(v), §36.11.
Encodings:: BibTeX

… ►

R. Bo and R. Wong (1994) Uniform asymptotic expansion of Charlier polynomials. Methods Appl. Anal. 1 (3), pp. 294–313.

ⓘ

External Links:: ISSN 1073-2772, Pdf, MathReview (Eberhard Wagner), ZentralBlatt
Referenced by:: §18.24.
Encodings:: BibTeX

… ►

J. Brüning (1984) On the asymptotic expansion of some integrals. Arch. Math. (Basel) 42 (3), pp. 253–259.

ⓘ

External Links:: ISSN 0003-889X, Document, MathReview (E. Riekstiņš), ZentralBlatt
Referenced by:: §2.5(ii).
Encodings:: BibTeX

…

9: Bibliography M

… ►

A. J. MacLeod (1993) Chebyshev expansions for modified Struve and related functions. Math. Comp. 60 (202), pp. 735–747.

ⓘ

External Links:: ISSN 0025-5718, FullText, MathReview, ZentralBlatt
Referenced by:: 2nd item.
Encodings:: BibTeX

… ►

A. J. MacLeod (2002a) Asymptotic expansions for the zeros of certain special functions. J. Comput. Appl. Math. 145 (2), pp. 261–267.

ⓘ

External Links:: ISSN 0377-0427, Document, MathReview (Andrea Laforgia), ZentralBlatt
Referenced by:: §10.70, §11.4(vii), §6.13.
Encodings:: BibTeX

… ►

J. P. McClure and R. Wong (1978) Explicit error terms for asymptotic expansions of Stieltjes transforms. J. Inst. Math. Appl. 22 (2), pp. 129–145.

ⓘ

External Links:: ISSN 0020-2932, Document, MathReview (G. M. Habibullah), ZentralBlatt
Referenced by:: §2.6(ii).
Encodings:: BibTeX

… ►

H. J. W. Müller (1966c) On asymptotic expansions of ellipsoidal wave functions. Math. Nachr. 32, pp. 157–172.

ⓘ

External Links:: Document, MathReview (F. M. Arscott), ZentralBlatt
Referenced by:: §29.11, §29.7(ii).
Encodings:: BibTeX

… ►

B. T. M. Murphy and A. D. Wood (1997) Hyperasymptotic solutions of second-order ordinary differential equations with a singularity of arbitrary integer rank. Methods Appl. Anal. 4 (3), pp. 250–260.

ⓘ

External Links:: ISSN 1073-2772, MathReview (W. Balser), ZentralBlatt
Referenced by:: §2.11(v).
Encodings:: BibTeX

…