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- W3210651710 abstract "In the paper, the authors establish nice Maclaurin series expansions andseries identities for powers of the inverse sine function, for powers of theinverse hyperbolic sine function, for composites of incomplete gamma functionswith the inverse hyperbolic sine function, for powers of the inverse tangentfunction, and for powers of the inverse hyperbolic tangent function, in termsof the first kind Stirling numbers, binomial coefficients, and multiple sums,apply the nice Maclaurin series expansion for powers of the inverse sinefunction to derive an explicit formula for special values of the second kindBell polynomials and to derive a series representation of the generalizedlogsine function, and deduce several combinatorial identities involving thefirst kind Stirling numbers. Some of these results simplify and unify someknown ones. All the Maclaurin series expansions of powers of the inversetrigonometric functions can be used to derive infinite series representationsof corresponding powers of the constant Pi." @default.
- W3210651710 created "2021-11-08" @default.
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- W3210651710 date "2021-01-26" @default.
- W3210651710 modified "2023-09-23" @default.
- W3210651710 title "Maclaurin series expansions for positive integer powers of inverse (hyperbolic) sine and tangent functions and for incomplete gamma functions with applications" @default.
- W3210651710 hasPublicationYear "2021" @default.
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