## 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.## References

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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