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

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

In this article, by virtue of expansions of two finite products of finitely many square sums, with the aid of series expansions of composite functions of (hyperbolic) sine and cosine functions with inverse sine and cosine functions, and in the light of properties of partial Bell polynomials, the aut...

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Bibliographic Details
Main Author: Qi Feng
Format: Article
Language:English
Published: De Gruyter 2022-10-01
Series:Demonstratio Mathematica
Subjects:
taylor’s series expansion
maclaurin’s series expansion
real power
inverse cosine function
inverse hyperbolic cosine function
inverse sine function
inverse hyperbolic sine function
stirling number of the first kind
combinatorial identity
composite
series representation
circular constant
partial bell polynomial
closed-form formula
riemann zeta function
primary 41a58
secondary 05a19
11b73
11b83
11c08
11s05
12d05
26a24
26c05
33b10
Online Access:https://doi.org/10.1515/dema-2022-0157

Internet

https://doi.org/10.1515/dema-2022-0157

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