Contiguous relations of hypergeometric series
经典分析与常微分方程
2013-10-04 v4
摘要
The 15 Gauss contiguous relations for hypergeometric series imply that any three 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.
引用
@article{arxiv.math/0109222,
title = {Contiguous relations of hypergeometric series},
author = {Raimundas Vidunas},
journal= {arXiv preprint arXiv:math/0109222},
year = {2013}
}
备注
12 pages; full bibliography added. This is the published text, with corrected formulas (24)-(25)