Bounds for the ratio of two gamma functions.
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TLDR
A long history of bounding the ratio for and, various origins of this topic are clarified, several developed courses are followed, different results are compared, useful methods are summarized, new advances are presented, some related problems are pointed out, and related references are collected as discussed by the authors.Abstract:
By looking back at the long history of bounding the ratio for and , various origins of this topic are clarified, several developed courses are followed, different results are compared, useful methods are summarized, new advances are presented, some related problems are pointed out, and related references are collected.read more
Citations
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Quadratic transformation inequalities for Gaussian hypergeometric function.
TL;DR: Several quadratic transformation inequalities for Gaussian hypergeometric function are presented and the analogs of duplication inequalities for the generalized Grötzsch ring function are found.
Journal ArticleDOI
Sharp Bounds for the Weighted Hölder Mean of the Zero-Balanced Generalized Complete Elliptic Integrals
TL;DR: In this article, the best possible bounds for the weighted Holder mean of the generalized complete elliptic integrals of the first and second kinds are presented, which are generalizations of previous results for complete p-elliptic integral integrals.
Journal ArticleDOI
Monotonicity and convexity involving generalized elliptic integral of the first kind
TL;DR: In this article, the monotonicity properties of the ratio between generalized elliptic integral of the first kind and its approximation for generalized Grotzsch ring function were studied, and the convexity properties of their difference were shown.
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Small deviations for beta ensembles
Michel Ledoux,Brian Rider +1 more
TL;DR: In this article, the authors established various small deviation inequalities for the extremal (soft edge) eigenvalues in the beta-Hermite and beta-Laguerre ensembles.
References
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Reference BookDOI
Asymptotics and Special Functions
TL;DR: A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool as discussed by the authors, and it can be found in many libraries.
Book
Basic Hypergeometric Series
George Gasper,Mizan Rahman +1 more
TL;DR: In this article, the Askey-Wilson q-beta integral and some associated formulas were used to generate bilinear generating functions for basic orthogonal polynomials.