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

被引：7

作者：

Qi, Feng ^{[1
,2
]}

Taylor, Peter ^{[2
]}

机构：

[1] Henan Polytech Univ, Sch Math & Informat, Jiaozuo 454010, Henan, Peoples R China

[2] Hulunbuir Univ, Sch Math & Phys, Hulunbuir 021008, Inner Mongolia, Peoples R China

来源：

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS | 2024年 / 18卷 / 01期

关键词：

Faa di Bruno formula; Series expansion; Power; Sinc function; Sinhc function; Partial Bell polynomial; Closed-form expression; Stirling number of the second kind; Central factorial number of the second kind; Weighted Stirling number of the second kind; Combinatorial proof; MODIFIED BESSEL-FUNCTIONS; COMPLETE MONOTONICITY; ABSOLUTE MONOTONICITY; JORDANS INEQUALITY; 1ST; REPRESENTATIONS; PROPERTY; NUMBERS;

D O I：

10.2298/AADM230902020Q

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper, with the aid of the Faadi 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.

引用

页码：92 / 115

页数：24

共 7 条

[1] Power Series Expansions of Real Powers of Inverse Cosine and Sine Functions, Closed-Form Formulas of Partial Bell Polynomials at Specific Arguments, and Series Representations of Real Powers of Circular Constant
Qi, Feng
SYMMETRY-BASEL, 2024, 16 (09):
[2] Specific values of partial Bell polynomials and series expansions for real powers of functions and for composite functions
Qi, Feng
Milovanovic, Gradimir, V
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[3] 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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DEMONSTRATIO MATHEMATICA, 2022, 55 (01) : 710 - 736
[4] 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
Guo, Bai-Ni
Lim, Dongkyu
Qi, Feng
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2022, 16 (02) : 427 - 466
[5] Series expansions of powers of arcsine, closed forms for special values of Bell polynomials, and series representations of generalized logsine functions
Guo, Bai-Ni
Lim, Dongkyu
Qi, Feng
AIMS MATHEMATICS, 2021, 6 (07): : 7494 - 7517
[6] General Closed-Form Transfer Function Expressions for Fast Filter Bank
Hao, Jinguang
Wang, Honggang
Wang, Lili
Liu, Xuefeng
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2023, E106A (10) : 1354 - 1357
[7] CLOSED-FORM FORMULAS, DETERMINANTAL EXPRESSIONS, RECURSIVE RELATIONS, POWER SERIES, AND SPECIAL VALUES OF SEVERAL FUNCTIONS USED IN CLARK-ISMAIL'S TWO CONJECTURES
Li, Yan-Fang
Lim, Dongkyu
Qi, Feng
APPLIED AND COMPUTATIONAL MATHEMATICS, 2023, 22 (04) : 443 - 465

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