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
نویسندگان
چکیده
In the paper, authors find series expansions and identities for positive integer powers of inverse (hyperbolic) sine tangent, composite incomplete gamma function with hyperbolic sine, in terms first kind Stirling numbers, apply a newly established expansion to derive closed-form formula specific partial Bell polynomials representation generalized logsine function, deduce combinatorial involving numbers.
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Universal Approximator Property of the Space of Hyperbolic Tangent Functions
In this paper, first the space of hyperbolic tangent functions is introduced and then the universal approximator property of this space is proved. In fact, by using this space, any nonlinear continuous function can be uniformly approximated with any degree of accuracy. Also, as an application, this space of functions is utilized to design feedback control for a nonlinear dynamical system.
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ژورنال
عنوان ژورنال: Applicable Analysis and Discrete Mathematics
سال: 2022
ISSN: ['1452-8630', '2406-100X']
DOI: https://doi.org/10.2298/aadm210401017g