Bounds for novel extended beta and hypergeometric functions and related results

Autor:	Rakesh K. Parmar, Tibor K. Pogány
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	Extended beta function Extended hypergeometric-type function Upper bounds for special functions MacDonald function Probability distribution Moments Mathematics QA1-939
Zdroj:	Journal of Inequalities and Applications, Vol 2024, Iss 1, Pp 1-11 (2024)
Druh dokumentu:	article
ISSN:	1029-242X
DOI:	10.1186/s13660-024-03148-8
Popis:	Abstract We introduce a new unified extension of the integral form of Euler’s beta function with a MacDonald function in the integrand and establish functional upper bounds for it. We use this definition to extend as well the Gaussian and Kummer’s confluent hypergeometric functions, for which we provide bounding inequalities. Moreover, we use our extension of the beta function to define a new probability distribution, for which we establish raw moments and moment inequalities and, as by-products, Turán inequalities for the initially defined extended beta function.
Databáze:	Directory of Open Access Journals
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