Contiguous relations of hypergeometric series

Details Contiguous relations of hypergeometric series Contiguous relations of hypergeometric series

2001-09-28

arxiv.org/abs/math/0109222v4

J. Comp. Appl. Math., Vol. 153 (2003), pg. 507-519

Mathematics

Classical Analysis and ODEs

12 pages; full bibliography added. This is the published text, with corrected formulas (24)-(25)

Scientific paper

The 15 Gauss contiguous relations for ${}_2F_1$ hypergeometric series imply that any three ${}_2F_1$ 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.

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