摘要
在泰勒展开的基础上理解卷积型级数的Mbius反演,给出了若干对反演系数,并应用于讨论已有的特殊函数,导出了它们的级数反演形式.
The modified Moebius inversion of convolution-type infinite series is justified based on the Taylor series expansion of analytic functions. A series of expansion and inversion coefficient pairs are given. A preliminary application to the special functions, e.g. spherical Bessel functions, Laguerre polynomials, hypergeometric functions and confluent hypergeometric functions, are made to deduce the inversions of their functional relations, including the multiplication and addition formulas.
出处
《大学物理》
北大核心
2012年第3期1-4,8,共5页
College Physics
关键词
泰勒展开
卷积型级数
Mbius反演
特殊函数
Taylor series expansion
infinite series of convolution character
Moebius inversion
special functions