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Legendre functions

  • Wilhelm Magnus
  • Fritz Oberhettinger
  • Raj Pal Soni
Part of the Die Grundlehren der mathematischen Wissenschaften book series (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

  1. Erdélyi, A.: Higher transcendental functions, Vol. 1. New York: McGraw-Hill 1953.Google Scholar
  2. Hobson, E. W.: The theory of spherical and ellipsoidal harmonics. Cambridge 1931.Google Scholar
  3. Heine, E.: Theorie der Kugelfunktionen, 2. vols. Berlin: G. Riemer 1878, 1881.Google Scholar
  4. Lense, J.: Kugelfunktionen. Leipzig: Akademische Verlagsgesellschaft 1950.zbMATHGoogle Scholar
  5. MacRobert, T. M.: Spherical harmonics. Methuen 1947.Google Scholar
  6. Prashad, G.: A treatise on spherical harmonics and the functions of Bessel and Lamé. Benares Math. Soc. 2 vols. 1930, 1932.Google Scholar
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  8. Snow, C.: Hypergeometric and Legendre functions with applications to integral equations and potential theory. National Bureau of Standards, Washington, D. C. 1951.Google Scholar
  9. Whittaker, E. T., and G. N. Watson: A course of modern analysis. Cambridge 1944.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1966

Authors and Affiliations

  • Wilhelm Magnus
    • 1
  • Fritz Oberhettinger
    • 2
  • Raj Pal Soni
    • 3
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityUSA
  2. 2.Oregon State UniversityUSA
  3. 3.International Business Machines CorporationUSA

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