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A Short Note on Integral Transformations and Conversion Formulas for Sequence Generating Functions
Axioms, 2019 The purpose of this note is to provide an expository introduction to some more curious integral formulas and transformations involving generating functions.
Maxie D. Schmidt
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Recurrent identities for two special functions of hypergeometric type
Вестник Самарского университета: Естественнонаучная серия, 2023 The article presents conclusions and proofs of Gauss-type identities for two known hypergeometric type functions. For the derivation and justification of formulas, the representation of functions in the form of a series is used, as well as an integral ...
Svetlana V. Podkletnova
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Completely monotonic functions involving the gamma and $q$-gamma functions [PDF]
Proceedings of the American Mathematical Society, 2005 The authors provide new examples of logarithmically completely monotonic functions. These examples are ratios of products involving the Gamma function or the \(q\)-Gamma function. As an application of these results new examples of infinitely divisible probability distributions can be obtained.
Grinshpan, Arcadii Z. +1 more
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Generalized Extended Matrix Variate Beta and Gamma Functions and Their Applications
Ingeniería y Ciencia, 2016 In this article, we define and study generalized forms of extended matrix variate gamma and beta functions. By using a number of results from matrix algebra, special functions of matrix arguments and zonal polynomials we derive a number of properties of ...
Daya K. Nagar +2 more
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New extension of beta, Gauss and confluent hypergeometric functions
Cumhuriyet Science Journal, 2021 There are many extensions and generalizations of Gamma and Beta functions in the literature. However, a new extension of the extended Beta function B_(ζ〖, α〗_1)^(α_2;〖 m〗_1,〖 m〗_2 ) (a_1,a_2 ) was introduced and presented here because of its important ...
Umar Muhammad Abubakar +1 more
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On the Nonlinear Integro-Differential Equations
Fractal and Fractional, 2021 The goal of this paper is to study the uniqueness of solutions of several nonlinear Liouville–Caputo integro-differential equations with variable coefficients and initial conditions, as well as an associated coupled system in Banach spaces.
Chenkuan Li, Joshua Beaudin
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Inverses of Gamma Functions [PDF]
Constructive Approximation, 2014 Euler's Gamma function $ $ either increases or decreases on intervals between two consequtive critical points. The inverse of $ $ on intervals of increase is shown to have an extension to a Pick-function and similar results are given on the intervals of decrease, thereby answering a question by Uchiyama. The corresponding integral representations are
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A refinement of a double inequality for the gamma function
, 2011 In the paper, we present a monotonicity result of a function involving the gamma function and the logarithmic function, refine a double inequality for the gamma function, and improve some known results for bounding the gamma function.Comment: 8 ...
Guo, Bai-Ni, Qi, Feng
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Some Gamma Function Inequalities [PDF]
Mathematics of Computation, 1993 A class of completely monotonic functions are presented involving the gamma function as well as the derivative of the psi function. As a consequence, new upper and lower bounds for the ratio Γ ( x + 1 ) / Γ ( x + s ) \Gamma (x + 1)/\Gamma (x
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A completely monotonic function involving the tri- and tetra-gamma functions
, 2010 The psi function $\psi(x)$ is defined by $\psi(x)=\frac{\Gamma'(x)}{\Gamma(x)}$ and $\psi^{(i)}(x)$ for $i\in\mathbb{N}$ denote the polygamma functions, where $\Gamma(x)$ is the gamma function.
Guo, Bai-Ni, Qi, Feng
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