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

DOI10.1080/10652460902867718zbMath1183.33010OpenAlexW1987057171MaRDI QIDQ3651163

Yu. A. Brychkov

Publication date: 8 December 2009

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460902867718

zbMATH Keywords

hypergeometric functionstrigonometric functionspower seriesBernoulli numbersspecial functionsdifferentiationEuler numbersBernoulli polynomialsEuler polynomials

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (6)

Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to \(\pi^{-1}\) ⋮ MacLaurin’s series expansions for positive integer powers of inverse (hyperbolic) sine and tangent functions, closed-form formula of specific partial Bell polynomials, and series representation of generalized logsine function ⋮ Identities involving Bernoulli and Euler polynomials ⋮ Three notes on Ser's and Hasse's representations for the zeta-functions ⋮ Taylor's series expansions for real powers of two functions containing squares of inverse cosine function, closed-form formula for specific partial Bell polynomials, and series representations for real powers of pi ⋮ On some properties of the generalized Bernoulli and Euler polynomials

Cites Work

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