Bounds for the Ratio of Two Gamma Functions

By Feng Qi (祁锋). 2009

258 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d3af055a80db478fa4ea98cc565f7df9cbafc366

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On Some Inequalities for the Gamma Function (2013, methodology): “The importance of this paper, also in order to fix the priority of the results, has already been pointed out by Feng Qi [17].”
Refinements of lower bounds for polygamma functions (2009, background): “For more information on this topic, please refer to the expository and survey article [15] and plenty of closely related references therein.”
Monotonicity and convexity involving generalized elliptic integral of the first kind (2021, background): “is the Pochhammer symbol and (x) = ∫ ∞ 0 t x−1e−t dt [12,17,18,29] is the classical Euler gamma function.”
PhaseMax: Convex Phase Retrieval via Basis Pursuit (2016, methodology): “Finally, by using bounds on ratios of Gamma functions [51], we obtain the bounds in (24) for real-valued vectors.”
Small deviations for beta ensembles (2009, unknown): “8) of [17].”
Stick-Breaking Policy Learning in Dec-POMDPs (2015, methodology): “his difﬁcult, we use grid search. To make the search more efﬁcient, we use the bounds of ( a+x) ( x) to give an initial estimate of the searching range. The bounds are from Wendel’s double Inequality [30]. x(x+ a)a 1 ( a+ x)=( x) xa (26) where x;a>0. B Some Basics of Stick-breaking Priors Here we”
Sharp Bounds for the Weighted Hölder Mean of the Zero-Balanced Generalized Complete Elliptic Integrals (2020, unknown): “(a + n − 1) = (a + n) (a) for n ∈ N, (x) = ∫ ∞ 0 t x−1e−t dt is the classical Euler gamma function [13,15,28, 33,35].”
Refinements, Generalizations, and Applications of Jordan's Inequality and Related Problems (2009, background): “For detailed information on the class of completely monotonic functions, please see the survey paper [66] and related references therein.”
Asymptotic formulae associated with the Wallis power function and digamma function (2013, background): “The inequalities (2) to (3) have attracted much interest of many mathematicians and have motivated a large number of research papers involving various generalizations and improvements, see [15] and an overview in [16] and the references cited therein.”