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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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Inverses of Gamma Functions [PDF]
Constructive Approximation, 2014 Euler's Gamma function $Γ$ either increases or decreases on intervals between two consequtive critical points. The inverse of $Γ$ 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.
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A Note on Gamma Functions [PDF]
Mathematical Notes, 1959 Various improvements in the formulawhich was discovered by Wallis in 1669, were studied by D. K. Kazarinoff in No. 40 of these Notes (December 1956).
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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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On the Multiple Gamma-Functions
Tokyo Journal of Mathematics, 1998 The authors obtain generalizations of the Shintani type infinite product representations for the \(r\)-ple gamma functions \(\Gamma_r(w;\widetilde\omega)\) and \(r\)-ple Stirling's modular forms \(\rho_r(\widetilde\omega)\) in the sense of Barnes. As an application, ``a simple proof'' of the inversion formulas of theta-function and Dedekind \(\eta ...
KATAYAMA, Koji, OHTSUKI, Makoto
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Optimal bounds for the generalized Euler–Mascheroni constant
Journal of Inequalities and Applications, 2018 We provide several sharp upper and lower bounds for the generalized Euler–Mascheroni constant. As consequences, some previous bounds for the Euler–Mascheroni constant are improved.
Ti-Ren Huang +3 more
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Some Inequalities of Extended Hypergeometric Functions
Mathematics, 2021 Hypergeometric functions and their inequalities have found frequent applications in various fields of mathematical sciences. Motivated by the above, we set up certain inequalities including extended type Gauss hypergeometric function and confluent ...
Shilpi Jain +3 more
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AxiomsHilbert-type inequalities derive from the classical Hilbert inequality, and their theoretical work has key applications not only in operator theory but also in various analytic disciplines.
Yong Hong, Qian Zhao, Zhihong Zhao
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Increasing property and logarithmic convexity of functions involving Dirichlet lambda function
Demonstratio Mathematica, 2023 In this article, with the help of an integral representation of the Dirichlet lambda function, by means of a monotonicity rule for the ratio of two integrals with a parameter, and by virtue of complete monotonicity and another property of an elementary ...
Qi Feng, Lim Dongkyu
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