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

In the paper, the authors find series expansions and identities for positive integer powers of inverse (hyperbolic) sine and tangent, for composite of incomplete gamma function with inverse hyperbolic sine, in terms of the first kind Stirling numbers, apply a newly established series expansion to de...

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Published inApplicable analysis and discrete mathematics Vol. 16; no. 2; pp. 427 - 466
Main Authors Guo, Bai-Ni, Lim, Dongkyu, Qi, Feng
Format Journal Article
LanguageEnglish
Published University of Belgrade, Serbia 01.10.2022
Online AccessGet full text
ISSN1452-8630
2406-100X
2406-100X
DOI10.2298/AADM210401017G

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Summary:In the paper, the authors find series expansions and identities for positive integer powers of inverse (hyperbolic) sine and tangent, for composite of incomplete gamma function with inverse hyperbolic sine, in terms of the first kind Stirling numbers, apply a newly established series expansion to derive a closed-form formula for specific partial Bell polynomials and to derive a series representation of generalized logsine function, and deduce combinatorial identities involving the first kind Stirling numbers.
ISSN:1452-8630
2406-100X
2406-100X
DOI:10.2298/AADM210401017G