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11: Bibliography D

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A Practical Guide to Splines. Revised edition, Applied Mathematical Sciences, Vol. 27, Springer-Verlag, New York.

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ISBN 0-387-95366-3, MathReview (Gerlind Plonka-Hoch), ZentralBlatt

Referenced by:

§3.11(vi).

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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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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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Olver’s error bound methods applied to linear ordinary differential equations having a simple turning point. Anal. Appl. (Singap.) 12 (4), pp. 385–402.

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ISSN 0219-5305, Document, Link, MathReview (Thomas Mbah Acho), ZentralBlatt

Referenced by:

5th item, §14.32.

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12: 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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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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Asymptotic expansions of Mellin transforms and analogues of Watson’s lemma. SIAM J. Math. Anal. 16 (4), pp. 896–906.

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

Referenced by:

§2.3(vi).

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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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Uniform asymptotic expansions of Hermite polynomials. M. Phil. thesis, City University of Hong Kong.

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Abstract

Referenced by:

§18.16(v).

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13: Bibliography B

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Asymptotic expansions of the modified Bessel function of the third kind of imaginary order. SIAM J. Appl. Math. 15, pp. 1315–1323.

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ISSN 0036-1399, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.45.

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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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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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Asymptotic Expansions for the Coefficient Functions Associated with Linear Second-order Differential Equations: The Simple Pole Case. In Asymptotic and Computational Analysis (Winnipeg, MB, 1989), R. Wong (Ed.), Lecture Notes in Pure and Applied Mathematics, Vol. 124, pp. 53–73.

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MathReview (John S. Lew), ZentralBlatt

Referenced by:

§2.8(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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14: Bibliography R

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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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Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. II. The general theory. Studies in Appl. Math. 53, pp. 217–224.

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MathReview (T. W. Kao), ZentralBlatt

Referenced by:

§2.8(iii).

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Applied Bessel Functions. Dover Publications Inc., New York.

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Notes:

Reprint of original Blackie & Son Limited, London, 1946.

External Links:

MathReview, ZentralBlatt

Referenced by:

§10.73(iii).

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The umbral calculus. Pure and Applied Mathematics, Vol. 111, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York.

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ISBN 0-12-594380-6, MathReview (R. Askey)

Referenced by:

§18.2(xii).

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Principles of Mathematical Analysis. 3rd edition, McGraw-Hill Book Co., New York.

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Notes:

International Series in Pure and Applied Mathematics

External Links:

MathReview, ZentralBlatt

Referenced by:

§1.4(iii).

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15: Bibliography V

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Computational Frameworks for the Fast Fourier Transform. Frontiers in Applied Mathematics, Vol. 10, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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ISBN 0-89871-285-8, MathReview (S. Hitotumatu), ZentralBlatt

Referenced by:

§3.11(v).

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Symbolic evaluation of coefficients in Airy-type asymptotic expansions. J. Math. Anal. Appl. 269 (1), pp. 317–331.

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ISSN 0022-247X, Document, MathReview, ZentralBlatt

Referenced by:

§2.4(v).

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A note on the asymptotic expansion of generalized hypergeometric functions. Anal. Appl. (Singap.) 12 (1), pp. 107–115.

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ISSN 0219-5305, Document, MathReview (Roberto S. Costas-Santos), ZentralBlatt

Referenced by:

§16.11(ii), §16.11(ii).

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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation. Constr. Approx. 20 (1), pp. 39–54.

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ISSN 0176-4276, Document, MathReview, ZentralBlatt

Referenced by:

§30.16(i), §30.16(ii), §30.16(ii).

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Asymptotic expansion of the generalized hypergeometric function ${}_p{}^{}F_q^{}(z)$ as $z\to \mathrm{\infty }$ for . Anal. Appl. (Singap.) 21 (2), pp. 535–545.

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ISSN 0219-5305, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§16.11(i), §16.11, Erratum (V1.1.9) for Section 16.11(i).

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16: Bibliography C

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Asymptotic expansion of the first elliptic integral. SIAM J. Math. Anal. 16 (5), pp. 1072–1092.

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ISSN 0036-1410, Document, MathReview (Kusum Soni), ZentralBlatt

Referenced by:

§19.27(ii), §19.27(vi), §19.9(ii), §2.5(ii).

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Asymptotic estimates for generalized Stirling numbers. Analysis (Munich) 20 (1), pp. 1–13.

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ISSN 0174-4747, MathReview (F. T. Howard), ZentralBlatt

Referenced by:

§26.8(vii).

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Uniform asymptotic expansion of an integral with a saddle point, a pole and a branch point. Proc. Roy. Soc. London Ser. A 426, pp. 273–286.

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ISSN 0080-4630, FullText, MathReview, ZentralBlatt

Referenced by:

§2.4(vi).

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On the asymptotic expansion of Airy’s integral. Proc. Glasgow Math. Assoc. 6, pp. 113–115.

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External Links:

Document, MathReview (L. Berg), ZentralBlatt

Referenced by:

(9.5.7), §9.5(ii).

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Asymptotic Expansions. Cambridge Tracts in Mathematics and Mathematical Physics, Cambridge University Press, New York.

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MathReview (A. E. Danese), ZentralBlatt

Referenced by:

Ch.2.

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17: Bibliography G

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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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Computation of the modified Bessel function of the third kind of imaginary orders: Uniform Airy-type asymptotic expansion. J. Comput. Appl. Math. 153 (1-2), pp. 225–234.

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ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§10.45, §10.74(viii).

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Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

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Notes:

Includes Fortran program claiming 12S accuracy

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ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt

Referenced by:

3rd item, §10.77(ix).

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Numerical Analysis of Spectral Methods: Theory and Applications. Society for Industrial and Applied Mathematics, Philadelphia, PA.

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Notes:

CBMS-NSF Regional Conference Series in Applied Mathematics, No. 26

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MathReview (O. Widlund), ZentralBlatt

Referenced by:

§18.38(i).

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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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18: 25.12 Polylogarithms

… ►The remainder of the equations in this subsection apply to principal branches. … ►For real or complex $s$ and $z$ the polylogarithm ${\mathrm{Li}}_s\left(z\right)$ is defined by … ►and … ►In terms of polylogarithms … ►For a uniform asymptotic approximation for $F_s(x)$ see Temme and Olde Daalhuis (1990).

19: Bibliography K

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Asymptotic expansions of certain $q$-series and a formula of Ramanujan for specific values of the Riemann zeta function. Acta Arith. 107 (3), pp. 269–298.

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ISSN 0065-1036, Document, Link, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§17.2(i).

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The asymptotic expansion of a hypergeometric function ${}_2{}^{}F_2^{}(1,\alpha ;{\rho }_1,{\rho }_2;z)$ . Math. Comp. 26 (120), pp. 963.

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FullText, MathReview, ZentralBlatt

Referenced by:

§16.11(ii), §16.11(ii).

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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.

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ISSN 0266-5611, Document, MathReview (Shun Shimomura), ZentralBlatt

Referenced by:

§32.11(iv).

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Electromagnetic Fields and Relativistic Particles. International Series in Pure and Applied Physics, McGraw-Hill Book Co., New York.

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ISBN 0-07-035264-X, MathReview (George Zipfel, Jr.)

Referenced by:

§1.17(ii), §10.73(ii).

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Strong asymptotics of polynomials orthogonal with respect to Freud weights. Internat. Math. Res. Notices 1999 (6), pp. 299–333.

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ISSN 1073-7928, Document, MathReview (Heinrich Begehr), ZentralBlatt

Referenced by:

§18.32.

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