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Bounds for novel extended beta and hypergeometric functions and related results
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Journal Article
Bounds for novel extended beta and hypergeometric functions and related results
2024
Overview
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.
Publisher
Springer International Publishing,Springer Nature B.V,SpringerOpen
Subject
