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On the finite sum representations of the Lauricella functions F D

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Abstract

By using divided differences, we derive two different ways of representing the Lauricella function of n variables F (n)D (a,b 1,b 2,. . .,b n;c;x 1,x 2,. . .,x n) as a finite sum, for b 1,b 2,. . .,b n positive integers, and a,c both positive integers or both positive rational numbers with c−a a positive integer.

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Authors and Affiliations

  1. Institute of Applied Mathematics, College of Sciences and CAD/CG Division, College of Computer & Information, Hefei University of Technology, Hefei, 230009, P. R. China

    Jieqing Tan

  2. Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University,, Antigonish, NS, Canada, B2G 2W5

    Ping Zhou

Authors
  1. Jieqing Tan
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  2. Ping Zhou
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Correspondence to Jieqing Tan.

Additional information

Communicated by C.A. Micchelli

AMS subject classification

33D45, 40B05, 40C99

Jieqing Tan: Research supported by the National Natural Science Foundation of China under Grant No. 10171026 and Anhui Provincial Natural Science Foundation under Grant No. 03046102.

Ping Zhou: Corresponding author. Research supported by NSERC of Canada.

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Tan, J., Zhou, P. On the finite sum representations of the Lauricella functions F D . Adv Comput Math 23, 333–351 (2005). https://doi.org/10.1007/s10444-004-1838-0

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  • DOI: https://doi.org/10.1007/s10444-004-1838-0

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