关于欧拉求和函数的微分及应用

Differential of Euler Summation Function and Its Application

针对文献[1]中的一些重要结论,在Hurwitz zeta函数部分和的积分渐进公式研究的基础上,研究了欧拉求和函数的推广的微分问题。采用解析数论中函数和级数的积分方法,对于Hurwitz zeta函数部分和进行微分,得出了欧拉求和函数推广公式的一阶和二阶微分公式,即定理1和定理2,将其结论进行应用,推出了关于级数和积分的五个恒等式,即推论1、推论2和推论3。

Aiming at some important conclusions in reference[1],differential of Euler summation function promotion was studied based on Hurwitz Zeta function partial sum and integral asymptotic formula.By using integral method of function and series in analytic number theory,partial sum of Hurwitz zeta function was differentiated,and the first and second order differential formula of Euler summation function promotion formula,namely Theorem 1 and Theorem 2 were obtained.The conclusions were applied to educe five identities of series and integral,that is Corollary 1,Corollary 2 and Corollary 3.