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Landen inequalities for a class of hypergeometric functions with applications [PDF]
Mathematical Inequalities & Applications, 2018 Summary: In this paper, we study a class of Gaussian hypergeometric function \(_2F_1(a,b;(a+b+1)/2;x)(a,b > 0)\), and find the maximal regions of \(ab\) plane in the first quadrant where the wellknown Landen identities for the complete elliptic integrals of the first kind turn on respective inequalities valid for each \(x \in (0,1)\).
Wang, Miao-Kun, Chu, Yu-Ming
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Remarks on Slater's asymptotic expansions of Kummer functions for large values of the $a-$parameter [PDF]
, 2013 In Slater's 1960 standard work on confluent hypergeometric functions, also called Kummer functions, a number of asymptotic expansions of these functions can be found. We summarize expansions derived from a differential equation for large values of the $a-
Temme, Nico M
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Radial fractional Laplace operators and Hessian inequalities
, 2012 In this paper we deduce a formula for the fractional Laplace operator $(-\Delta)^{s}$ on radially symmetric functions useful for some applications. We give a criterion of subharmonicity associated with $(-\Delta)^{s}$, and apply it to a problem related
Ferrari, Fausto, Verbitsky, Igor E.
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Miskolc Mathematical NotesRecently, an enormous amount of effort has been devoted to extending the gamma and beta functions because of their nice properties and interesting applications. The contribution of this paper falls within this framework.
Mustapha Raïssouli, Mohamed Chergui
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Shape invariant hypergeometric type operators with application to quantum mechanics
, 2006 A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators.
A.F. Nikiforov +6 more
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Alexandria Engineering JournalThis study aims to investigate the properties of fractional calculus theory (FCT) in the complex domain. We focus on the relationship between the theories of special functions (SFT) and FCT, which have seen recent advancements and have led to various ...
F. Ghanim +3 more
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, 2012 A series expansion for Heckman-Opdam hypergeometric functions $\varphi_\lambda$ is obtained for all $\lambda \in \mathfrak a^*_{\mathbb C}.$ As a consequence, estimates for $\varphi_\lambda$ away from the walls of a Weyl chamber are established.
Narayanan, E. K. +2 more
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Moments of Dirichlet splines and their applications to hypergeometric functions
Journal of Computational and Applied Mathematics, 1994 Dirichlet averages of multivariate functions are employed for a derivation of basic recurrence formulas for the moments of multivariate Dirichlet splines. An algorithm for computing the moments of multivariate simplex splines is presented. Applications to hypergeometric functions of several variables are discussed.
Neuman, Edward, Van Fleet, Patrick J.
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Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications
International Journal of Mathematics and Mathematical Sciences, 2012 This paper deals with recent developments of Hilbert-type discrete and integral inequalities by introducing kernels, weight functions, and multiparameters.
Lokenath Debnath, Bicheng Yang
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Four Families of Summation Formulas for 4F3(1) with Application
AxiomsA collection of functions organized according to their indexing based on non-negative integers is grouped by the common factor of fixed integer N. This grouping results in a summation of N series, each consisting of functions partitioned according to ...
Belakavadi Radhakrishna Srivatsa Kumar +2 more
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