Summation of certain trigonometric series with logarithmic coefficients

被引：0

作者：

Rufus Boyack

机构：

[1] University of Alberta,Department of Physics & Theoretical Physics Institute

来源：

The Journal of Analysis | 2022年 / 30卷

关键词：

Trigonometric series; Logarithmic coefficients; Digamma function; Frullani’s theorem; 42A20; 42A24; 42A32;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The sums of three trigonometric series with logarithmic coefficients are derived by extending an approach first utilized by Lerch. By applying Frullani’s theorem to two of these series, two non-trivial integrals involving hyperbolic functions are evaluated in terms of the digamma function.

引用

页码：119 / 129

页数：10

共 7 条

[1]

Tricković SB(2008)On the summation of trigonometric series Integral Transforms and Special Functions 19 441-undefined

[2]

Vidanović MV(1897)Über eine Formel aus der Theorie der Gammafunction Monatshefte für Mathematik und Physik 8 187-undefined

[3]

Stanković MS(1895)Sur une relation ayant rapports avec la theorie de la fonction gamma Bulletin International de l’Académie des Sciences Prague 2 214-undefined

[4]

Lerch M(2013)On gamma quotients and infinite products Advances in Applied Mathematics 51 546-undefined

[5]

Lerch M(undefined)undefined undefined undefined undefined-undefined

[6]

Chamberland M(undefined)undefined undefined undefined undefined-undefined

[7]

Straub A(undefined)undefined undefined undefined undefined-undefined

← 1 →