Hypergeometric series with gamma product formula
Hypergeometric series with gamma product formula
复制标题
具有伽玛乘积公式的超几何级数
DOI：
10.1016/j.indag.2016.12.001
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Katsunori Iwasaki
中科院分区：
文献类型：
--
作者：
M. Ito;M. Noumi;Katsunori Iwasaki
本文对带一个自由参数的非终止超几何求和进行了理论研究。综合复分析与渐近分析、超越曲线的几何与算术、无理数的有理逼近等多种方法，得到了超几何和容许Gamma积公式的算术味的必要条件.即使在高斯超几何级数最经典的情况下，这种研究似乎也是新的。
We develop a theoretical study of non-terminating hypergeometric summations with one free parameter. Composing various methods in complex and asymptotic analysis, geometry and arithmetic of certain transcendental curves and rational approximations of irrational numbers, we are able to obtain some necessary conditions of arithmetic flavor for a given hypergeometric sum to admit a gamma product formula. This kind of research seems to be new even in the most classical case of the Gauss hypergeometric series.