Contiguous relations of hypergeometric series

By Raimundas Vidunas. 2001

59 citations recorded by the source corpus.

The 15 Gauss contiguous relations for 2F1 hypergeometric series imply that any three 2F1 series whose corresponding parameters differ by integers are linearly related (over the field of rational functions in the parameters). We prove several properties of coefficients of these general contiguous relations, and use the results to propose effective ways to compute contiguous relations. We also discuss contiguous relations of generalized and basic hypergeometric functions, and several applications of them.

Subfields: Algebra and Number Theory, Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d8a2e6b0f888993f4370c21eb3fc5fe392bca089

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In Algebra and Number Theory

1. Medhat Ahmed Rakha
2. Arjun Kumar Rathie

In Applied Mathematics

1. Medhat Ahmed Rakha
2. Arjun Kumar Rathie

In Computational Theory and Mathematics

1. Medhat Ahmed Rakha
2. Arjun Kumar Rathie

Citations in the corpus

• Generalizations of classical summation theorems for the series 2 F 1 and 3 F 2 with applications (2011, background): “Moreover, a finite sum expression for 2F1 contiguous to Kummer summation formula is also given by formula (2) by Vidunas [19] obtained by other means.”