Laplace%20method%20for%20asymptotic%20expansions%20of%20integrals

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1: Bibliography N

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On an asymptotic expansion of the Kontorovich-Lebedev transform. Methods Appl. Anal. 3 (1), pp. 98–108.

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ISSN 1073-2772, FullText, MathReview (C. M. Joshi), ZentralBlatt

Referenced by:

§10.43(v).

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Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.

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FullText, MathReview (I. A. Stegun), ZentralBlatt

Referenced by:

§19.37(iv).

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Uniform asymptotic expansion for the incomplete beta function. SIGMA Symmetry Integrability Geom. Methods Appl. 12, pp. 101, 5 pages.

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ISSN 1815-0659, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§8.18(ii), §8.18(ii), Erratum (V1.0.14) for Subsections 8.18(ii)–8.11(v).

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An explicit formula for the coefficients in Laplace’s method. Constr. Approx. 38 (3), pp. 471–487.

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ISSN 0176-4276, Document, Link, MathReview (Pedro J. Pagola), ZentralBlatt

Referenced by:

§5.11(i), §5.11(i).

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An extension of Laplace’s method. Constr. Approx. 51 (2), pp. 247–272.

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ISSN 0176-4276, Document, Link, MathReview (José Luis López), ZentralBlatt

Referenced by:

(11.11.16), (11.11.17), §11.11(iii).

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2: Bibliography S

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Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.

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External Links:

Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§28.8(iv).

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Uniform asymptotic expansions of modified Mathieu functions. J. Reine Angew. Math. 247, pp. 1–17.

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MathReview (J. Meixner), ZentralBlatt

Referenced by:

§28.8(iv).

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A simple approach to asymptotic expansions for Fourier integrals of singular functions. Appl. Math. Comput. 216 (11), pp. 3378–3385.

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ISSN 0096-3003, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§2.3(iv).

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Exact error terms in the asymptotic expansion of a class of integral transforms. I. Oscillatory kernels. SIAM J. Math. Anal. 11 (5), pp. 828–841.

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ISSN 0036-1410, Document, MathReview (John S. Lew), ZentralBlatt

Referenced by:

§2.5(ii).

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Numerical Methods Based on Sinc and Analytic Functions. Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.

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Notes:

Sinc-Pack, a set of 480 Matlab programs with a 470-page tutorial, is available for purchase from SINC, LLC by contacting Frank Stenger.

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ISBN 0-387-94008-1, MathReview (B. Boyanov), ZentralBlatt

Referenced by:

§3.3(vi), §3.4(i), §3.5(i).

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3: Bibliography B

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Chapter 13 of Ramanujan’s second notebook: Integrals and asymptotic expansions. Expo. Math. 2 (4), pp. 289–347.

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ISSN 0723-0869, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§2.10(iii).

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Asymptotic Expansions of Integrals. Holt, Rinehart, and Winston, New York.

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Notes:

Reprinted with corrections by Dover Publications Inc., New York, 1986

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ISBN 0-486-65082-0, MathReview, ZentralBlatt

Referenced by:

§2.3(ii), §2.3(v), §2.4(iv), §2.4(v), §2.5(iii), §2.5(ii), Ch.2, Ch.9.

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Uniform asymptotic expansion of Charlier polynomials. Methods Appl. Anal. 1 (3), pp. 294–313.

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ISSN 1073-2772, Pdf, MathReview (Eberhard Wagner), ZentralBlatt

Referenced by:

§18.24.

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Approximations for the late coefficients in asymptotic expansions arising in the method of steepest descents. Methods Appl. Anal. 2 (4), pp. 475–489.

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ISSN 1073-2772, Pdf, MathReview (Dan Polis̆evski), ZentralBlatt

Referenced by:

§2.4(iv).

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

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ISSN 0003-889X, Document, MathReview (E. Riekstiņš), ZentralBlatt

Referenced by:

§2.5(ii).

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4: Bibliography K

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Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

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Document, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.18(i).

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An indirect method for evaluating certain infinite integrals. Z. Angew. Math. Phys. 29 (3), pp. 380–386.

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ISSN 0044-2275, Document, MathReview, ZentralBlatt

Referenced by:

§10.71(ii).

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Exponentially accurate uniform asymptotic approximations for integrals and Bleistein’s method revisited. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 469 (2153), pp. 20130008, 12.

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ISSN 1364-5021, Document, FullText, MathReview (Ulrich D. Jentschura), ZentralBlatt

Referenced by:

§2.4(vi), §2.4(vi).

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Two new asymptotic methods in the theory of wave propagation in inhomogeneous media. Sov. Phys. Acoust. 14, pp. 1–17.

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ISSN 0038-562X

Referenced by:

§36.14(iv).

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A Handbook of Methods of Approximate Fourier Transformation and Inversion of the Laplace Transformation. Mir, Moscow.

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Notes:

Translated from the Russian by George Yankovsky. Reprint of the 1977 translation

External Links:

MathReview, ZentralBlatt

Referenced by:

§3.5(viii).

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5: 11.6 Asymptotic Expansions

§11.6 Asymptotic Expansions

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§11.6(i) Large $|z|$, Fixed $\nu$

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§11.6(ii) Large $|\nu |$, Fixed $z$

… ►More fully, the series (11.2.1) and (11.2.2) can be regarded as generalized asymptotic expansions (§2.1(v)). …

6: Bibliography D

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Asymptotic Methods in Analysis. 2nd edition, Bibliotheca Mathematica, Vol. IV, North-Holland Publishing Co., Amsterdam.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§2.2, Ch.2, §26.7(iv), §26.7(iv), §4.13.

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On the high-order coefficients in the uniform asymptotic expansion for the incomplete gamma function. Methods Appl. Anal. 5 (3), pp. 223–247.

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ISSN 1073-2772, Pdf, MathReview (John G. Stalker), ZentralBlatt

Referenced by:

§8.12.

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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.

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Notes:

(This reference has several typographical errors.)

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

Referenced by:

§13.21(ii), §13.21(iii), §13.21(iv).

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Uniform asymptotic approximation of Mathieu functions. Methods Appl. Anal. 1 (2), pp. 143–168.

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ISSN 1073-2772, Pdf, MathReview (J. M. H. Peters), ZentralBlatt

Referenced by:

§28.8(iv).

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Error analysis in a uniform asymptotic expansion for the generalised exponential integral. J. Comput. Appl. Math. 80 (1), pp. 127–161.

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ISSN 0377-0427, Document, MathReview (Eberhard Wagner), ZentralBlatt

Referenced by:

§2.11(iii), §8.20(ii).

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7: Bibliography O

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On the resurgence properties of the uniform asymptotic expansion of the incomplete gamma function. Methods Appl. Anal. 5 (4), pp. 425–438.

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

Referenced by:

§8.12.

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On the asymptotics for late coefficients in uniform asymptotic expansions of integrals with coalescing saddles. Methods Appl. Anal. 7 (4), pp. 727–745.

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

Referenced by:

§36.12(iii).

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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.

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Document, MathReview (J. Todd), ZentralBlatt

Referenced by:

§10.21(vii).

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Uniform, exponentially improved, asymptotic expansions for the generalized exponential integral. SIAM J. Math. Anal. 22 (5), pp. 1460–1474.

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

Referenced by:

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

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Asymptotic expansions of the coefficients in asymptotic series solutions of linear differential equations. Methods Appl. Anal. 1 (1), pp. 1–13.

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

Referenced by:

§2.7(ii), §2.7(ii).

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8: Bibliography G

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On high precision methods for computing integrals involving Bessel functions. Math. Comp. 33 (147), pp. 1049–1057.

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ISSN 0025-5718, FullText, MathReview (K. Jetter), ZentralBlatt

Referenced by:

§10.74(vii).

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On the generalization of a method for computing Bessel function integrals. J. Comput. Appl. Math. 6 (2), pp. 167–168.

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ISSN 0771-050X, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vii).

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Exactification of the Poincaré asymptotic expansion of the Hankel integral: spectacularly accurate asymptotic expansions and non-asymptotic scales. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 470 (2162), pp. 20130529, 16.

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ISSN 1364-5021, Document, Link, MathReview (Eugenia N. Petropoulou), ZentralBlatt

Referenced by:

§10.22(v), §10.22(v).

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A method for evaluating certain Bessel integrals. Z. Angew. Math. Phys. 30 (4), pp. 722–723.

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ISSN 0044-2275, Document, MathReview

Referenced by:

§10.71(ii).

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Asymptotische Entwicklungen für unvollständige Gammafunktionen. Forum Math. 3 (2), pp. 105–141 (German).

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Notes:

Translated title: Asymptotic expansions for incomplete gamma functions.

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ISSN 0933-7741, MathReview (T. Erber), ZentralBlatt

Referenced by:

§8.16.

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