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

共 50 条

[41] SERIES OF TRIGONOMETRIC FUNCTIONS
KIRKHAM, D
DEDOELDE.PJ
AMERICAN MATHEMATICAL MONTHLY, 1964, 71 (10): : 1141 - &
[42] ON MEAN VALUES OF INTEGRAL FUNCTIONS + THEIR DERIVATIVES DEFINED BY DIRICHLET SERIES
GUPTA, JS
AMERICAN MATHEMATICAL MONTHLY, 1964, 71 (05): : 520 - &
[43] ON MEAN VALUES OF INTEGRAL FUNCTIONS AND THEIR DERIVATIVES REPRESENTED BY DIRICHLET SERIES
SRIVASTA.SN
COMPOSITIO MATHEMATICA, 1968, 19 (04) : 334 - &
[44] LINEAR DEPENDENCE OF CERTAIN TRIGONOMETRIC VALUES
CARLITZ, L
HEUER, K
HEUER, GA
AMERICAN MATHEMATICAL MONTHLY, 1975, 82 (02): : 169 - 171
[45] Rational values of trigonometric functions
不详
AMERICAN MATHEMATICAL MONTHLY, 2007, 114 (09): : 818 - 818
[46] CERTAIN RESULTS ON A CLASS OF INTEGRAL FUNCTIONS REPRESENTED BY MULTIPLE DIRICHLET SERIES
Dua, Nibha
Kumar, Niraj
MATEMATICKI VESNIK, 2020, 72 (03): : 226 - 231
[47] SPACE OF ANALYTIC-FUNCTIONS REPRESENTABLE BY A CERTAIN CLASS OF DIRICHLET SERIES
KHAPLANOV, MG
SIBERIAN MATHEMATICAL JOURNAL, 1976, 17 (05) : 843 - 857
[48] On certain Dirichlet series built from the Fourier coefficients of modular functions
Kohnen, W
PACIFIC JOURNAL OF MATHEMATICS, 2004, 215 (01) : 29 - 33
[49] EXPLICIT FORMULAS FOR A CLASS OF DIRICHLET SERIES
REDMOND, D
PACIFIC JOURNAL OF MATHEMATICS, 1982, 102 (02) : 413 - 435
[50] ON THE CRITICAL-VALUES OF CERTAIN DIRICHLET SERIES AND THE PERIODS OF AUTOMORPHIC-FORMS
SHIMURA, G
INVENTIONES MATHEMATICAE, 1988, 94 (02) : 245 - 305

← 1 2 3 4 5 →