expansions in Mathieu functions

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31: Bibliography T

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Uniform asymptotic expansions of confluent hypergeometric functions. J. Inst. Math. Appl. 22 (2), pp. 215–223.

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ISSN 0020-2932, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§13.8(ii), §13.8(ii).

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The asymptotic expansion of the incomplete gamma functions. SIAM J. Math. Anal. 10 (4), pp. 757–766.

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ISSN 0036-1410, Document, MathReview (E. Riekstiņš), ZentralBlatt

Referenced by:

§8.12.

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Uniform asymptotic expansions of a class of integrals in terms of modified Bessel functions, with application to confluent hypergeometric functions. SIAM J. Math. Anal. 21 (1), pp. 241–261.

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ISSN 0036-1410, Document, MathReview (Pablo Martín), ZentralBlatt

Referenced by:

§13.8(iii), §13.8(iii).

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Asymptotic expansions of Kummer hypergeometric functions with three asymptotic parameters a, b and z. Indagationes Mathematicae.

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ISSN 0019-3577, Document, Link

Referenced by:

§13.8(iv).

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Special functions in phase space: Mathieu functions. J. Phys. A 31 (31), pp. 6725–6739.

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ISSN 0305-4470, Document, MathReview (Bing Hong Wang), ZentralBlatt

Referenced by:

8th item.

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32: Bibliography J

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Further results on the computation of incomplete gamma functions. In Analytic Theory of Continued Fractions, II (Pitlochry/Aviemore, 1985), W. J. Thron (Ed.), Lecture Notes in Math. 1199, pp. 67–89.

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MathReview (Marietta J. Tretter), ZentralBlatt

Referenced by:

§8.25(iv).

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Fonctions de Mathieu et polynômes de Klein-Gordon. C. R. Acad. Sci. Paris Sér. I Math. 325 (7), pp. 713–716 (French).

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Notes:

Translated title: Mathieu functions and Klein-Gordon polynomials.

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ISSN 0764-4442, Document, MathReview, ZentralBlatt

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7th item.

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Fonctions de Mathieu et fonctions propres de l’oscillateur relativiste. Ann. Fac. Sci. Toulouse Math. (6) 7 (3), pp. 465–495 (French).

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Notes:

Translated title: Mathieu functions and eigenfunctions of the relativistic oscillator.

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ISSN 0240-2963, Pdf, MathReview (Jean-Michel Ghez), ZentralBlatt

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7th item.

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On the computation of incomplete gamma functions in the complex domain. J. Comput. Appl. Math. 12/13, pp. 401–417.

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ISSN 0377-0427, Document, MathReview (M. Marsden), ZentralBlatt

Referenced by:

§8.25(iv), §8.9.

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Asymptotic behavior of the continued fraction coefficients of a class of Stieltjes transforms including the Binet function. In Orthogonal functions, moment theory, and continued fractions (Campinas, 1996), Lecture Notes in Pure and Appl. Math., Vol. 199, pp. 257–274.

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MathReview (Olav Njåstad), ZentralBlatt

Referenced by:

§5.10, §5.10.

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33: Bibliography C

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On the expansion of a Coulomb potential in spherical harmonics. Proc. Cambridge Philos. Soc. 46, pp. 626–633.

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Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§34.12.

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Expansions in terms of parabolic cylinder functions. Proc. Edinburgh Math. Soc. (2) 8, pp. 50–65.

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MathReview (I. I. Hirschman, Jr.), ZentralBlatt

Referenced by:

§12.16.

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Painlevé Equations—Nonlinear Special Functions: Computation and Application. In Orthogonal Polynomials and Special Functions, F. Marcellàn and W. van Assche (Eds.), Lecture Notes in Math., Vol. 1883, pp. 331–411.

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ISBN 3-540-31062-2, MathReview (Marta Mazzocco), ZentralBlatt

Referenced by:

Ch.32.

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Chebyshev expansions for the Bessel function $J_n(z)$ in the complex plane. Math. Comp. 40 (161), pp. 343–366.

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ISSN 0025-5718, FullText, MathReview (C. W. Clenshaw), ZentralBlatt

Referenced by:

§10.76(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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34: Bibliography R

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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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3rd item.

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Mathieu functions of integral orders and real arguments. IEEE Trans. Microwave Theory Tech. 28 (3), pp. 276–277.

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Notes:

Includes Fortran program

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FullText

Referenced by:

§28.36(ii), §28.36(iii).

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Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function. Mathematics 9 (16).

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Link, ISSN 2227-7390, Document

Referenced by:

§8.15.

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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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On Simple Waves with Profiles in the form of some Special Functions—Chebyshev-Hermite, Mathieu, Whittaker—in Two-phase Media. In Differential Operators and Related Topics, Vol. I (Odessa, 1997), Operator Theory: Advances and Applications, Vol. 117, pp. 313–322.

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ISBN 3-7643-6287-1, MathReview Entry, ZentralBlatt

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5th item.

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35: Bibliography K

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Generalized functions. Mathematics in Science and Engineering, Vol. 171, Academic Press, Inc., Orlando, FL.

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Notes:

Theory and technique

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ISBN 0-12-396560-8, MathReview (Qing Yi Chen), ZentralBlatt

Referenced by:

§1.16(viii).

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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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Tables of values of the modified Mathieu functions. Math. Comp. 14, pp. 118–129.

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FullText, MathReview (L. J. Slater), ZentralBlatt

Referenced by:

5th item.

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Algebras of Virasoro type, the energy-momentum tensor, and operator expansions on Riemann surfaces. Funktsional. Anal. i Prilozhen. 23 (1), pp. 24–40 (Russian).

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Notes:

In Russian. English translation: Funct. Anal. Appl. 23(1989), no. 1, pp. 19–33

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ISSN 0374-1990, Document, MathReview (Fedor Malikov), ZentralBlatt

Referenced by:

§20.12(ii).

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