The hypergeometric function

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


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).*


Analytic Continuation Hypergeometric Function Negative Integer Legendre Function Transformation Formula 
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  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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