Contiguous relations of hypergeometric series

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 rel...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 153; no. 1-2; pp. 507 - 519
Main Author: VIDUNAS, Raimundas
Format: Journal Article Conference Proceeding
Language:English
Published: Amsterdam Elsevier B.V 01.04.2003
Elsevier
Subjects:
Contiguous relations
Exact sciences and technology
Hypergeometric function
Mathematical analysis
Mathematics
Sciences and techniques of general use
Special functions
Hypergeometric function
Contiguous relations
Hypergeometric series
Contiguous relation
Applied mathematics
Rational function
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(02)00643-X