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Polynomial series expansions for confluent and Gaussian hypergeometric functions


Authors: W. Luh, J. Müller, S. Ponnusamy and P. Vasundhra
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
Published electronically: March 15, 2005
MathSciNet review: 2164104
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Abstract | References | Similar Articles | Additional Information

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
Email: jmueller@uni-trier.de

S. Ponnusamy
Affiliation: Department of Mathematics, Indian Institute of Technology, IIT-Madras, Chennai- 600 036, India
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

DOI: https://doi.org/10.1090/S0025-5718-05-01734-5
Keywords: Hypergeometric series, Hadamard product, polynomial expansions
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).
Article copyright: © Copyright 2005 American Mathematical Society

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