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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Polynomial series expansions for confluent and Gaussian hypergeometric functions
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by W. Luh, J. Müller, S. Ponnusamy and P. Vasundhra PDF
Math. Comp. 74 (2005), 1937-1952 Request permission

Abstract:

Based on the Hadamard product of power series, polynomial series expansions for confluent hypergeometric functions $M(a,c;\cdot )$ and for Gaussian hypergeometric functions $F(a,b;c;\cdot )$ are introduced and studied. It turns out that the partial sums provide an interesting alternative for the numerical evaluation of the functions $M(a,c;\cdot )$ and $F(a,b;c;\cdot )$, in particular, if the parameters are also viewed as variables.
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Additional Information
  • W. Luh
  • Affiliation: University of Trier, FB IV, Mathematics, D-54286 Trier, Germany
  • Email: luh@uni-trier.de
  • J. Müller
  • Affiliation: University of Trier, FB IV, Mathematics, D-54286 Trier, Germany
  • ORCID: 0000-0002-5872-0129
  • Email: jmueller@uni-trier.de
  • S. Ponnusamy
  • Affiliation: Department of Mathematics, Indian Institute of Technology, IIT-Madras, Chennai- 600 036, India
  • MR Author ID: 259376
  • ORCID: 0000-0002-3699-2713
  • Email: samy@iitm.ac.in
  • P. Vasundhra
  • Affiliation: Department of Mathematics, Indian Institute of Technology, IIT-Madras, Chennai- 600 036, India
  • Email: vasu2kk@yahoo.com
  • Received by editor(s): December 3, 2003
  • Received by editor(s) in revised form: May 18, 2004
  • Published electronically: March 15, 2005
  • Additional Notes: The work of the authors was supported by DST-DAAD under Project Based Personal Exchange Programme (Sanction No. INT/DAAD/P-64/2002).
  • © Copyright 2005 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 1937-1952
  • MSC (2000): Primary 33C05, 33C15, 33F05, 65D20
  • DOI: https://doi.org/10.1090/S0025-5718-05-01734-5
  • MathSciNet review: 2164104