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The hypergeometric function

  • Wilhelm Magnus
  • Fritz Oberhettinger
  • Raj Pal Soni
Chapter
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 52)

Abstract

The function represented by the infinite series \(\sum\limits_{n = 0}^\infty {\frac{{{{(a)}_n}{{(b)}_n}}}{{{{(c)}_n}}}\frac{{{z^n}}}{{n!}}} \) within its circle of convergence and all the analytic continuations is called the hypergeometric function 2 F 1(a, b; c;z).*

Keywords

Analytic Continuation Hypergeometric Function Negative Integer Legendre Function Transformation Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature

  1. Erdélyi, A.: Higher transcendental functions, Vol. 1. New York: McGraw-Hill 1953.Google Scholar
  2. Kampé de Fériet, J.: La fonction hypergeometrique. Paris: Gauthiers-Villars 1937.Google Scholar
  3. Klein, F.: Vorlesungen über die hypergeometrische Funktion. Berlin: Teubner 1933.CrossRefGoogle Scholar
  4. MacRobert, T. M.: Proc. Edinburgh Math. Soc. 42 (1923) 84–88.CrossRefGoogle Scholar
  5. MacRobert, T. M.: Functions of a complex variable. London: Macmillan 1954.zbMATHGoogle 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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