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- [2] Series expansions of powers of arcsine, closed forms for special values of Bell polynomials, and series representations of generalized logsine functionsAIMS MATHEMATICS, 2021, 6 (07): : 7494 - 7517Guo, Bai-NiLim, DongkyuQi, Feng
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
被引：15
|作者：
Guo, Bai-Ni
[1
]
Lim, Dongkyu
[2
]
Qi, Feng
[3
]
机构：
[1] Henan Polytech Univ, Sch Math & Informat, Jiaozuo 454010, Henan, Peoples R China
[2] Andong Natl Univ, Dept Math Educ, Andong 36729, South Korea
[3] Tiangong Univ, Sch Math Sci, Tianjin 300387, Peoples R China
基金：
新加坡国家研究基金会;
关键词：
Maclaurin's series expansion;
inverse sine function;
partial Bell polynomial;
generalized logsine function;
first kind Stirling number;
INCOMPLETE GAMMA;
STIRLING NUMBERS;
INEQUALITIES;
EXPRESSIONS;
D O I：
10.2298/AADM210401017G
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：427 / 466
页数：40
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