On some new contiguous relations for the Gauss hypergeometric function with applications

Contiguous relations for hypergeometric series contain an enormous amount of hidden information. Applications of contiguous relations range from the evaluation of hypergeometric series to the derivation of summation and transformation formulas for such series. In this paper, a new set of contiguous...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2011-02, Vol.61 (3), p.620-629
Main Authors: Rakha, Medhat A., Rathie, Arjun K., Chopra, Purnima
Format: Article
Language:English
Subjects:
[formula omitted] Hypergeometric function
Contiguous function relation
Derivation
Gauss hypergeometric function
Hypergeometric functions
Linear recurrence relation
Mathematical analysis
Mathematical models
Transformations
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Summary:Contiguous relations for hypergeometric series contain an enormous amount of hidden information. Applications of contiguous relations range from the evaluation of hypergeometric series to the derivation of summation and transformation formulas for such series. In this paper, a new set of contiguous function relations are established. Applications of such relations to hypergeometric summation formulas and the theory of Jacobi polynomials are presented.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2010.12.008