Rocky Mountain Journal of Mathematics

A Generalization of Kummer's Identity

Raimundas Vidunas

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Rocky Mountain J. Math., Volume 32, Number 2 (2002), 919-936.

First available in Project Euclid: 5 June 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 33C05: Classical hypergeometric functions, $_2F_1$
Secondary: 33F10: Symbolic computation (Gosper and Zeilberger algorithms, etc.) [See also 68W30] 39A10: Difference equations, additive


Vidunas, Raimundas. A Generalization of Kummer's Identity. Rocky Mountain J. Math. 32 (2002), no. 2, 919--936. doi:10.1216/rmjm/1030539701.

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  • G.E. Andrews, R. Askey and R. Roy, Special functions, Cambridge University Press, Cambridge, 1999.
  • W.N. Bailey, Generalized hypergeometric functions, Cambridge University Press, Cambridge, 1935.
  • A. Erdélyi, ed., Higher transcendental functions, volume I, McGraw-Hill Book Company, New York, 1953.
  • C. Fox, The expression of hypergeometric series in terms of similar series, Proc. London Math. Soc. 26 (1927), 201-210.
  • B. Gauthier, Calcul symbolique sur les séries hypergéométriques, Ph.D. thesis, l'Univ. de Marne-la-Valeé, 1999.
  • R.W. Gosper, A letter to D. Stanton, XEROX Palo Alto Research Center, 8 September 1980.
  • G.H. Hardy, Ramanujan. Twelve lectures on subjects suggested by his life and work, Cambridge University Press, Cambridge, 1940.
  • W. Koepf, Hypergeometric summation, Vieweg, Wiesbaden, 1998.
  • --------, Computer algebra package hsum.mpl for Maple,\~koepf/research.html, 1999.
  • T.H. Koornwinder, Identities of nonterminating series by Zeilberger's algorithm, J. Comput. Appl. Math. 99 (1998), 449-461.
  • E.E. Kummer, Ueber die hypergeometrische Reihe, J. für Math. 15 (1836), 39-83.
  • M. Petkov\usek, H.S. Wilf and D. Zeilberger, $A=B$, A.K. Peters, Wellesley, Massachusetts, 1996.
  • K.S. Rao, J. van der Jeugt, J. Raynal, R. Jagannathan and V. Rajeswari, Group-theoretical basis for the terminating $_3F_2(1)$ series, J. Phys. A 25 (1992), 861-876.
  • J. Thomae, Ueber die Funktionen welche durch Reihen von der Form dargestellt werden: $1+\fracpp^\p p^\pp1q^\p q^\pp+\cdots$, J. für Math. 87 (1879), 26-73.
  • R. Vidunas and T.H. Koornwinder, Web page of the NWO project, Algorithmic methods for special functions by computer algebra,\~thk/specfun/compalg.html, 2000.
  • F.J.W. Whipple, A group of generalized hypergeometric series: Relations between $120$ allied series of type $F\left[\smallmatrix a,b,c\\ e,f\endsmallmatrix\right]$, Proc. London Math. Soc. 23 (1924), 104-114.
  • --------, On series allied to the hypergeometric series with argument $-1$, Proc. London Math. Soc. 30 (1930), 81-94.
  • D. Zeilberger, Computer algebra package EKHAD for Maple, \noindent\~zeilberg/programs.html, 1999.