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

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 and for Gaussian hypergeometric functions are introduced and studied. It turns out that the partial sums provide an interesting alternative for the numerical evaluation of the functions and , 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