Extended Prudnikov sum

AIMS Mathematics

article

Robert Reynolds¹  Allan Stauffer¹ 

[1] Department of Mathematics and Statistics, York University

关键词: finite sum;    finite product;    trigonometric function;    Catalan's constant;    Hurwitz-Lerch Zeta function;    Cauchy integral;   

DOI  :  10.3934/math.20221021

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

A Prudnikov sum is extended to derive the finite sum of the Hurwitz-Lerch Zeta function in terms of the Hurwitz-Lerch Zeta function. This formula is then used to evaluate a number trigonometric sums and products in terms of other trigonometric functions. These sums and products are taken over positive integers which can be simplified in certain circumstances. The results obtained include generalizations of linear combinations of the Hurwitz-Lerch Zeta functions and involving powers of 2 evaluated in terms of sums of Hurwitz-Lerch Zeta functions. Some of these derivations are in the form of a new recurrence identity and finite products of trigonometric functions.

【 授权许可】

CC BY