Values of certain Dirichlet series and higher derivative formulas of trigonometric functions

被引：0

作者：

Lanphier, Dominic ^{[1
]}

Lin, Allen ^{[2
]}

机构：

[1] Western Kentucky Univ, Dept Math, 1906 Coll Hts Blvd,11078, Bowling Green, KY 42101 USA

[2] MIT, 77 Massachusetts Ave, Cambridge, MA 02139 USA

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2024年 / 20卷 / 04期

关键词：

Dirichlet series; Bernoulli numbers; Bernoulli polynomials; Eulerian numbers; Euler polynomials; EULER; TRANSCENDENCE; BERNOULLI;

D O I：

10.1142/S1793042124500519

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We determine new values of certain Dirichlet series and related infinite series. These formulas extend results of several authors. To obtain these results we apply recent expansions of higher derivative formulas of trigonometric functions. We also investigate the transcendentality of values of these series and arithmetic relations of the values of certain related infinite series.

引用

页码：995 / 1016

页数：22

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