SERIES EXPANSIONS FOR POWERS OF SINC FUNCTION AND CLOSED-FORM EXPRESSIONS FOR SPECIFIC PARTIAL BELL POLYNOMIALS

In the paper, with the aid of the Faà di Bruno formula, in terms of the central factorial numbers and the Stirling numbers of the second kinds, the authors derive several series expansions for any positive integer powers of the sinc and sinhc functions, discover several closed-form expressions for p...

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Bibliographic Details
Published inApplicable analysis and discrete mathematics Vol. 18; no. 1; pp. 92 - 115
Main Authors Qi, Feng, Taylor, Peter
Format Journal Article
LanguageEnglish
Published University of Belgrade, Serbia 01.04.2024
Online AccessGet full text
ISSN1452-8630
2406-100X
2406-100X
DOI10.2298/AADM230902020Q

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Summary:In the paper, with the aid of the Faà di Bruno formula, in terms of the central factorial numbers and the Stirling numbers of the second kinds, the authors derive several series expansions for any positive integer powers of the sinc and sinhc functions, discover several closed-form expressions for partial Bell polynomials of all derivatives of the sinc function, establish several series expansions for any real powers of the sinc and sinhc functions, and present several identities for central factorial numbers of the second kind and for the Stirling numbers of the second kind.
ISSN:1452-8630
2406-100X
2406-100X
DOI:10.2298/AADM230902020Q