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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| Published in | Applicable analysis and discrete mathematics Vol. 18; no. 1; pp. 92 - 115 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
University of Belgrade, Serbia
01.04.2024
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| Online Access | Get full text |
| ISSN | 1452-8630 2406-100X 2406-100X |
| DOI | 10.2298/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. |
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| ISSN: | 1452-8630 2406-100X 2406-100X |
| DOI: | 10.2298/AADM230902020Q |