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Legendre functions

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Formulas and Theorems for the Special Functions of Mathematical Physics

Part of the book series: Die Grundlehren der mathematischen Wissenschaften ((GL,volume 52))

Abstract

The Legendre functions are solutions of the Legendre differential equation

$$(1 - {z^2})\frac{{{d^2}w}}{{d{z^2}}} - 2z\frac{{dw}}{{dz}} + [v(v + 1) - {\mu ^2}{(1 - {z^2})^{ - 1}}]w = 0$$

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Literature

  • Erdélyi, A.: Higher transcendental functions, Vol. 1. New York: McGraw-Hill 1953.

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  • Hobson, E. W.: The theory of spherical and ellipsoidal harmonics. Cambridge 1931.

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  • Heine, E.: Theorie der Kugelfunktionen, 2. vols. Berlin: G. Riemer 1878, 1881.

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  • Lense, J.: Kugelfunktionen. Leipzig: Akademische Verlagsgesellschaft 1950.

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  • MacRobert, T. M.: Spherical harmonics. Methuen 1947.

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  • Prashad, G.: A treatise on spherical harmonics and the functions of Bessel and Lamé. Benares Math. Soc. 2 vols. 1930, 1932.

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  • Robin, L.: Fonctions spheriques de Legendre et fonctions sphéroidales, 3 vols. Paris: Gauthier-Villars 1957–1959.

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  • Snow, C.: Hypergeometric and Legendre functions with applications to integral equations and potential theory. National Bureau of Standards, Washington, D. C. 1951.

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  • Whittaker, E. T., and G. N. Watson: A course of modern analysis. Cambridge 1944.

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Author information

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, USA

    Dr. Wilhelm Magnus (Professor)

  2. Oregon State University, USA

    Dr. Fritz Oberhettinger (Professor)

  3. International Business Machines Corporation, USA

    Dr. Raj Pal Soni (Mathematician)

Authors
  1. Dr. Wilhelm Magnus
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  2. Dr. Fritz Oberhettinger
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  3. Dr. Raj Pal Soni
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© 1966 Springer-Verlag Berlin Heidelberg

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Magnus, W., Oberhettinger, F., Soni, R.P. (1966). Legendre functions. In: Formulas and Theorems for the Special Functions of Mathematical Physics. Die Grundlehren der mathematischen Wissenschaften, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11761-3_4

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  • DOI: https://doi.org/10.1007/978-3-662-11761-3_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-11763-7

  • Online ISBN: 978-3-662-11761-3

  • eBook Packages: Springer Book Archive

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