Evaluation of convergent series by using finite parts

Open Journal of Mathematical Sciences

Ricardo Estrada¹ 

[1] Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.;

关键词: hadamard finite part limits;    summation of series;    hurwitz zeta function;    digamma function.;   

DOI  :  10.30538/oms2020.0099

来源: DOAJ

【 摘 要 】

We present a method to find the sum of a convergent series based on the computation of Hadamard finite part limits of partial sums. We give several illustrations, the main being the formulas for convergent series of the type \(\sum_{n=2}^{\infty}\frac{\left( -1\right) ^{n}\zeta\left( n,a\right) b^{n+k}}{n+k},\) where \(\zeta\left( s,a\right)\) is Hurwitz zeta function, \(\left\vert b\right\vert \leq\left\vert a\right\vert ,\) \(b\neq-a,\) and \(k\in\mathbb{N}.\)

【 授权许可】

Unknown