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11: Bibliography

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Asymptotic expansions of spheroidal wave functions. J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.

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MathReview (J. G. van der Corput), ZentralBlatt

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§30.9(iii).

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Uniform asymptotic expansions for exponential integrals $E_n(x)$ and Bickley functions ${\mathrm{Ki}}_n(x)$ . ACM Trans. Math. Software 9 (4), pp. 467–479.

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ISSN 0098-3500, Document, MathReview (Marietta J. Tretter), ZentralBlatt

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§10.43(iii).

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Repeated integrals and derivatives of $K$ Bessel functions. SIAM J. Math. Anal. 20 (1), pp. 169–175.

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ISSN 0036-1410, Document, MathReview (A. Haimovici), ZentralBlatt

Referenced by:

§10.43(iii).

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Special value of the hypergeometric function ${}_3{}^{}F_2^{}$ and connection formulae among asymptotic expansions. J. Indian Math. Soc. (N.S.) 51, pp. 161–221.

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ISSN 0019-5839, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§16.4(iii).

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Singularities of Differentiable Maps. Vol. II. Birkhäuser, Boston-Berlin.

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Monodromy and asymptotics of integrals, Translated from the Russian by Hugh Porteous, Translation revised by the authors and James Montaldi

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ISBN 0-8176-3185-2, MathReview, ZentralBlatt

Referenced by:

§36.12(iii).

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12: Bibliography W

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Asymptotic expansions for second-order linear difference equations with a turning point. Numer. Math. 94 (1), pp. 147–194.

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ISSN 0029-599X, Document, MathReview (Sergey M. Zagorodnyuk), ZentralBlatt

Referenced by:

§2.9(iii).

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

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Document, MathReview (L. Berg), ZentralBlatt

Referenced by:

§8.11(v).

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Asymptotic expansions of the Kontorovich-Lebedev transform. Appl. Anal. 12 (3), pp. 161–172.

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ISSN 0003-6811, Document, MathReview (E. R. Love), ZentralBlatt

Referenced by:

§10.43(v).

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Applications of some recent results in asymptotic expansions. Congr. Numer. 37, pp. 145–182.

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ISSN 0384-9864, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§19.27(vi).

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The asymptotic expansion of the generalized Bessel function. Proc. London Math. Soc. (2) 38, pp. 257–270.

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Document, ZentralBlatt

Referenced by:

§10.46.

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13: Bibliography D

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Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems. Constr. Approx. 40 (1), pp. 61–104.

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ISSN 0176-4276, Document, Link, MathReview (Francisco Marcellán), ZentralBlatt

Referenced by:

§2.9(iii), §2.9(iii).

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Asymptotic Expansions: Their Derivation and Interpretation. Academic Press, London-New York.

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External Links:

MathReview, ZentralBlatt

Referenced by:

(11.11.11), §11.6(i), §11.6(iii), §2.11(v), Ch.2, §8.1, Notations, Notations.

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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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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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Uniform asymptotic expansions for Charlier polynomials. J. Approx. Theory 112 (1), pp. 93–133.

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ISSN 0021-9045, Document, MathReview (Eberhard Wagner), ZentralBlatt

Referenced by:

§18.24.

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14: 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 expansions of integrals with stationary point near algebraic singularity. Comm. Pure Appl. Math. 19, pp. 353–370.

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Document, MathReview (J. G. van der Corput), ZentralBlatt

Referenced by:

§2.3(v).

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Uniform asymptotic expansions of integrals with many nearby stationary points and algebraic singularities. J. Math. Mech. 17, pp. 533–559.

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External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§36.12(iii).

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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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15: 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)). …

16: 25.12 Polylogarithms

… ►For real or complex $s$ and $z$ the polylogarithm ${\mathrm{Li}}_s\left(z\right)$ is defined by … ►

Integral Representation

… ►The Fermi–Dirac and Bose–Einstein integrals are defined by … ►In terms of polylogarithms … ►For a uniform asymptotic approximation for $F_s(x)$ see Temme and Olde Daalhuis (1990).

17: Bibliography R

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On the definition and properties of generalized $6$-$j$ symbols. J. Math. Phys. 20 (12), pp. 2398–2415.

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ISSN 0022-2488, Document, MathReview (S. Saran), ZentralBlatt

Referenced by:

§16.4(iii), §16.4(iii).

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High precision Chebyshev expansions for Airy functions and their derivatives. Technical report University of Birmingham Computer Centre.

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Referenced by:

3rd item.

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Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. I. Plane Couette flow. Studies in Appl. Math. 53, pp. 91–110.

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MathReview (T. W. Kao), ZentralBlatt

Referenced by:

§2.8(iii).

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Asymptotics and Bounds of the Roots of Equations (Russian). Zinatne, Riga.

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ISBN 5-7966-0570-4, MathReview (Guillermo López Lagomasino), ZentralBlatt

Referenced by:

§12.11(ii), §6.13.

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Partial fractions expansions and identities for products of Bessel functions. J. Math. Phys. 46 (4), pp. 043509–1–043509–18.

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ISSN 0022-2488, Document, MathReview (Wolfgang zu Castell), ZentralBlatt

Referenced by:

§10.23(ii).

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18: Bibliography L

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An asymptotic estimate for the Bernoulli and Euler numbers. Canad. Math. Bull. 20 (1), pp. 109–111.

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External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.11.

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A note on the uniform asymptotic expansion of integrals with coalescing endpoint and saddle points. J. Phys. A 19 (3), pp. 329–335.

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ISSN 0305-4470, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§2.4(vi).

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Uniform asymptotic expansions of symmetric elliptic integrals. Constr. Approx. 17 (4), pp. 535–559.

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ISSN 0176-4276, Document, MathReview (Valdir A. Menegatto), ZentralBlatt

Referenced by:

§19.27(vi).

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Asymptotic expansions of symmetric standard elliptic integrals. SIAM J. Math. Anal. 31 (4), pp. 754–775.

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ISSN 1095-7154, Document, MathReview (P. Anandani), ZentralBlatt

Referenced by:

§19.27(vi), §2.6(ii).

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Uniform asymptotic expansions at a caustic. Comm. Pure Appl. Math. 19, pp. 215–250.

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Document, MathReview (Colin Clark), ZentralBlatt

Referenced by:

§36.12(iii), §36.14(i).

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19: 2.11 Remainder Terms; Stokes Phenomenon

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§2.11(i) Numerical Use of Asymptotic Expansions

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§2.11(iii) Exponentially-Improved Expansions

… ►A simple example is provided by Euler’s transformation (§3.9(ii)) applied to the asymptotic expansion for the exponential integral (§6.12(i)): … ► …

20: Bibliography P

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The asymptotic behaviour of Pearcey’s integral for complex variables. Proc. Roy. Soc. London Ser. A 432 (1886), pp. 391–426.

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ISSN 0962-8444, Document, Link, MathReview (J. S. Joel), ZentralBlatt

Referenced by:

§36.12(i).

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Error bounds for the uniform asymptotic expansion of the incomplete gamma function. J. Comput. Appl. Math. 147 (1), pp. 215–231.

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ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§8.12.

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A uniform asymptotic expansion for the incomplete gamma function. J. Comput. Appl. Math. 148 (2), pp. 323–339.

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ISSN 0377-0427, Document, MathReview (Dumitru Acu), ZentralBlatt

Referenced by:

(8.11.6), §8.11(iii), (8.12.18), §8.12, §8.12, §8.12, Erratum (V1.0.16) for Equation (8.12.18).

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The asymptotic expansion of a generalised incomplete gamma function. J. Comput. Appl. Math. 151 (2), pp. 297–306.

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

Referenced by:

§8.16.

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Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.

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Notes:

Double-precision Fortran, maximum accuracy 20S.

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ISSN 0010-4655, Document, Code

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6th item.

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