由Dixon求和定理导出的超几何函数变换式

Hypergeometric transformations from Dixon's summation theorem

受Rathie和Rakha工作的启发,利用著名的Dixon求和定理建立一个主体变换式.从这个变换式出发,通过适当地选取参数推导出多个超几何函数的变换式.特别地,得到一个近似匹配的_5F_4-型超几何函数的封闭性求和式.

Inspired by the work of Rathie and Rakha, we establish a main theorem with the help of Dixon＇s summation theorem. From this theorem, we obtain several new hypergeometric transformations by some famous summation formulas. Especially, we obtain a new closed summation formula of a nearly-poised hypergeometric series 5F4 by gamma functions.