Asymptotic Expansion of Legendre Polynomials with Respect to the Index near x = 1: Generalization of the Mehler–Rayleigh Formula-Reference-Cited by-同舟云学术

Asymptotic Expansion of Legendre Polynomials with Respect to the Index near x = 1: Generalization of the Mehler–Rayleigh Formula

Published:2020-07 Issue:7 Volume:60 Page:1155-1162
ISSN:0965-5425
Container-title:Computational Mathematics and Mathematical Physics
language:en
Short-container-title:Comput. Math. and Math. Phys.

Author:

Bakaleinikov L. A.,Tropp E. A.

Publisher

Pleiades Publishing Ltd

Subject

Computational Mathematics

Link

https://link.springer.com/content/pdf/10.1134/S0965542520070027.pdf

Reference8 articles.

1. E. W. Hobson, The Theory of Spherical and Ellipsoidal Harmonics (Cambridge Univ. Press, Cambridge, 1931).

2. N. N. Lebedev, Special Functions and Their Applications (Fizmatgiz, Moscow, 1963; Prentice Hall, Englewood Cliffs, N.J., 1965).

3. R. C. Thorne, “The asymptotic expansion of Legendre functions of large degree and order,” Phil. Trans. R. Soc. London 249, 597–620 (1957).

4. F. G. Mehler, “Uber die Verteilung der statischen Elektrizität in einem von zwei Kugelkalotten begrenzten Körper,” J. Reine Angew. Math. 68, 134–150 (1868).

5. J. S. Rayleigh, “On the relation between the functions of Laplace and Bessel,” Proc. Math. Soc. London 9, 61–64 (1878).

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