利用无理函数变换构造新的无穷级数恒等式  

Using Unrational Function Transformation to Prove Infinite Series Identity

作　　者：张来萍 ZHANG Laiping(Xinhua College, Ningxia University, Yinchuan 750021, China)

机构地区：[1]宁夏大学新华学院,宁夏银川750021

出　　处：《河南教育学院学报（自然科学版）》2020年第2期1-8,共8页Journal of Henan Institute of Education(Natural Science Edition)

基　　金：宁夏大学新华学院科学研究基金资助(20XHKY07)。

摘　　要：用函数变换方法证明无穷级数恒等式,适当地选取无理函数,然后利用复变函数的留数基本定理和Mittag-Leffier展开定理,并通过代数运算得到一些形式各异的无穷级数恒等式。The infinite series identities were proved by function transformation method,irrational functions were selected appropriately,and then some infinite series identities with different forms were obtained by using the basic residue theorem and Mittag-Leffier expansion theorem of complex functions.

关 键 词：无理函数 留数 无穷级数 伽马函数 恒等式 

分 类 号：O174.5[理学—数学]