expansions in series of cross-products of Bessel functions and modified Bessel functions

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1: 28.24 Expansions in Series of Cross-Products of Bessel Functions or Modified Bessel Functions

§28.24 Expansions in Series of Cross-Products of Bessel Functions or Modified Bessel Functions

… ►For further power series of Mathieu radial functions of integer order for small parameters and improved convergence rate see Larsen et al. (2009).

2: Bibliography C

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CEPHES (free C library)

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Notes:: This library treats about 180 different mathematical functions, including a substantial collection of probability integrals, Bessel functions, and higher transcendental functions. Implementations in single, double, and quad precisions are provided. See Moshier (1989).
External Links:: GAMS (package CEPHES)
Referenced by:: § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.
Encodings:: BibTeX

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J. A. Cochran (1964) Remarks on the zeros of cross-product Bessel functions. J. Soc. Indust. Appl. Math. 12 (3), pp. 580–587.

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External Links:: Document, MathReview (M. J. O. Strutt), ZentralBlatt
Referenced by:: §10.21(x), §10.21(x).
Encodings:: BibTeX

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J. A. Cochran (1966a) The analyticity of cross-product Bessel function zeros. Proc. Cambridge Philos. Soc. 62, pp. 215–226.

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External Links:: MathReview (R. G. Langebartel), ZentralBlatt
Referenced by:: §10.21(x).
Encodings:: BibTeX

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J. A. Cochran (1966b) The asymptotic nature of zeros of cross-product Bessel functions. Quart. J. Mech. Appl. Math. 19 (4), pp. 511–522.

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External Links:: ISSN 0033-5614, Document, MathReview (F. W. J. Olver), ZentralBlatt
Referenced by:: §10.21(x).
Encodings:: BibTeX

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J. P. Coleman and A. J. Monaghan (1983) Chebyshev expansions for the Bessel function

J_{n}(z)

in the complex plane. Math. Comp. 40 (161), pp. 343–366.

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External Links:: ISSN 0025-5718, FullText, MathReview (C. W. Clenshaw), ZentralBlatt
Referenced by:: §10.76(ii).
Encodings:: BibTeX

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3: Bibliography S

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L. Z. Salchev and V. B. Popov (1976) A property of the zeros of cross-product Bessel functions of different orders. Z. Angew. Math. Mech. 56 (2), pp. 120–121.

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External Links:: Document, MathReview (S. Saran), ZentralBlatt
Referenced by:: §10.21(x).
Encodings:: BibTeX

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H. Shanker (1939) On the expansion of the parabolic cylinder function in a series of the product of two parabolic cylinder functions. J. Indian Math. Soc. (N. S.) 3, pp. 226–230.

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External Links:: ZentralBlatt
Referenced by:: §12.13(i).
Encodings:: BibTeX

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A. Sharples (1971) Uniform asymptotic expansions of modified Mathieu functions. J. Reine Angew. Math. 247, pp. 1–17.

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External Links:: MathReview (J. Meixner), ZentralBlatt
Referenced by:: §28.8(iv).
Encodings:: BibTeX

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S. L. Skorokhodov (1985) On the calculation of complex zeros of the modified Bessel function of the second kind. Dokl. Akad. Nauk SSSR 280 (2), pp. 296–299.

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Notes:: English translation in Soviet Math. Dokl. 31(1), pp. 78–81
External Links:: ISSN 0002-3264, MathReview (I. F. Kushnirchuk), ZentralBlatt
Referenced by:: §10.74(vi).
Encodings:: BibTeX