Power expansions of powers of trigonometric functions andseries containing Bernoulli and Euler polynomials

被引：15

作者：

Brychkov, Yu. A. ^{[1
]}

机构：

[1] Russian Acad Sci, Dorodnicyn Comp Ctr, Moscow 119639, Russia

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2009年 / 20卷 / 11期

关键词：

trigonometric functions; differentiation; power series; Bernoulli polynomials; Bernoulli numbers; Euler polynomials; Euler numbers; hypergeometric functions; special functions; summation;

D O I：

10.1080/10652460902867718

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Differentiation formulas and power expansions are derived for sinn z, cosn z, tann z and cotn z. Summation formulas containing Bernoulli and Euler polynomials and numbers are obtained.

引用

页码：797 / 804

页数：8

共 14 条

[1] Bernoulli polynomials and asymptotic expansions of the quotient of gamma functions
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[2] Euler–MacLaurin Summation Formula on Polytopes and Expansions in Multivariate Bernoulli Polynomials
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[3] Fourier expansions for higher-order Apostol–Genocchi, Apostol–Bernoulli and Apostol–Euler polynomials
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[4] Expansions over a Simplex of Real Functions by Means of Bernoulli Polynomials
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[5] Expansions over a simplex of real functions by means of Bernoulli polynomials
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[6] Euler-MacLaurin Summation Formula on Polytopes and Expansions in Multivariate Bernoulli Polynomials
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[7] Some identities on the Bernoulli, Euler and Genocchi polynomials via power sums and alternate power sums
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DISCRETE MATHEMATICS, 2009, 309 (10) : 3346 - 3363
[8] Fourier expansions for higher-order Apostol-Genocchi, Apostol-Bernoulli and Apostol-Euler polynomials
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ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
[9] Specific values of partial Bell polynomials and series expansions for real powers of functions and for composite functions
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FILOMAT, 2023, 37 (28) : 9469 - 9485
[10] Explicit polynomial expansions of regular real functions by means of even order Bernoulli polynomials and boundary values
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