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

DOI10.2298/AADM210401017GOpenAlexW4226267126WikidataQ115495152 ScholiaQ115495152MaRDI QIDQ5054093

Bai-Ni Guo, Dongkyu Lim, Feng Qi

Publication date: 29 November 2022

Published in: Applicable Analysis and Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2298/aadm210401017g

zbMATH Keywords

partial Bell polynomialinverse sine functionMaclaurin's series expansiongeneralized logsine functionfirst kind Stirling number

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Combinatorial identities, bijective combinatorics (05A19) Gamma, beta and polygamma functions (33B15) Polynomials in number theory (11C08) Special sequences and polynomials (11B83) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Denjoy and Perron integrals, other special integrals (26A39) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20) Exponential and trigonometric functions (33B10)

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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

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