asymptotic approximation of integrals

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11: 14.26 Uniform Asymptotic Expansions

… ►See also Frenzen (1990), Gil et al. (2000), Shivakumar and Wong (1988), Ursell (1984), and Wong (1989) for uniform asymptotic approximations obtained from integral representations.

12: 2.6 Distributional Methods

§2.6 Distributional Methods

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§2.6(ii) Stieltjes Transform

… ►Corresponding results for the generalized Stieltjes transform …An application has been given by López (2000) to derive asymptotic expansions of standard symmetric elliptic integrals, complete with error bounds; see §19.27(vi). … ►For rigorous derivations of these results and also order estimates for ${\delta }_n(x)$, see Wong (1979) and Wong (1989, Chapter 6).

13: 9.10 Integrals

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§9.10(ii) Asymptotic Approximations

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14: 2.5 Mellin Transform Methods

§2.5 Mellin Transform Methods

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§2.5(ii) Extensions

… ►The first reference also contains explicit expressions for the error terms, as do Soni (1980) and Carlson and Gustafson (1985). … ►See also Brüning (1984) for a different approach. …

15: 25.12 Polylogarithms

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$G_s(x)={\mathrm{Li}}_{s+1}\left({\mathrm{e}}^x\right).$

►For a uniform asymptotic approximation for $F_s(x)$ see Temme and Olde Daalhuis (1990).

16: Bibliography W

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On uniform asymptotic expansion of definite integrals. J. Approximation Theory 7 (1), pp. 76–86.

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External Links:

Document, MathReview (L. Berg), ZentralBlatt

Referenced by:

§8.11(v).

Encodings:

BibTeX

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Asymptotic Approximations of Integrals. Academic Press Inc., Boston-New York.

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Notes:

Reprinted with corrections by SIAM, Philadelphia, PA, 2001.

External Links:

ISBN 0-12-762535-6, MathReview (F. Ursell), ZentralBlatt

Referenced by:

§1.14(iv), §1.14(vii), §1.15(iv), §1.16(i), §1.16(ii), §1.16(iii), §1.16(iv), §1.16(v), §1.16(vi), §1.16(vii), §1.16(viii), §14.26, Ch.14, §2.10(iv), §2.3(i), §2.3(ii), §2.3(iii), §2.3(v), §2.4(i), §2.4(ii), §2.4(iv), §2.4(v), §2.4(vi), §2.5(iii), §2.5(i), §2.5(ii), §2.5(ii), §2.5(ii), §2.5(iii), §2.6(iii), §2.6(i), §2.6(i), §2.6(ii), §2.6(ii), §2.6(iii), §2.6(iv), §2.6(iv), Ch.2, §7.20(i), Ch.8, Ch.9, Profile Roderick S. C. Wong.

Encodings:

BibTeX

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17: Bibliography K

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Asymptotic approximations for the first incomplete elliptic integral near logarithmic singularity. J. Comput. Appl. Math. 205 (1), pp. 186–206.

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External Links:

ISSN 0377-0427, Document, FullText, MathReview (José Luis López), ZentralBlatt

Referenced by:

§19.12, §19.12, §19.36(iv), §19.36(iv).

Encodings:

BibTeX

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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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External Links:

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

Referenced by:

§2.4(vi), §2.4(vi).

Encodings:

BibTeX

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18: Bibliography T

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Uniform asymptotic approximation of Fermi-Dirac integrals. J. Comput. Appl. Math. 31 (3), pp. 383–387.

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External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§25.12(iii).

Encodings:

BibTeX

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19: Bibliography C

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Asymptotic approximations for symmetric elliptic integrals. SIAM J. Math. Anal. 25 (2), pp. 288–303.

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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

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20: 2.10 Sums and Sequences

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The first infinite integral in (2.10.2) converges.

… ►This identity can be used to find asymptotic approximations for large $n$ when the factor $v_j$ changes slowly with $j$, and $u_j$ is oscillatory; compare the approximation of Fourier integrals by integration by parts in §2.3(i). …