Results 41 to 50 of about 39,748 (165)
Hypergeometric Functions for Function Fields
Finite Fields and Their Applications, 1995 Let \(\{a,b,c\}\) be complex constants. Then the famous Gauss hypergeometric equation is given by \[ z(1 - z) {d^2y \over dz^2} + \bigl( c - (a + b + 1) z \bigr) {dy \over dz} - aby = 0. \] One defines the Pochhammer symbol \((a)_n\) by \((a)_0 : = 1\) and for \(n > 1\), \((a)_n : = a(a + 1) (a + 2) (a + 3) \cdots (a + n - 1)\).
openaire +1 more source
On Extensions of Extended Gauss Hypergeometric Function
Communications in Advanced Mathematical Sciences, 2019 The aim of this paper is to introduce a new extensions of extended Gauss hypergeometric function. Certain integral representations, transformation and summation formulas for extended Gauss hypergeometric function are presented and some special cases are ...
Ahmed Ali Atash +2 more
doaj +1 more source
GENERALIZATION OF EXTENDED BETA FUNCTION, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS [PDF]
Honam Mathematical Journal, 2011 Summary: The main object of this paper is to present generalization of extended beta function, extended hypergeometric and confluent hypergeometric function introduced by Chaudhry et al. and obtained various integral representations, properties of beta function, Mellin transform, beta distribution, differentiation formulas, transform formulas ...
Lee, Dong Myung +3 more
openaire +2 more sources
Summation formulas for Fox-Wright function [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 By means of inversion techniques and several known hypergeometric series identities, summation formulas for Fox-Wright function are explored. They give some new hypergeometric series identities when the parameters are specified.
Chuanan Wei, Lily Li Liu, Dianxuan Gong
doaj +1 more source
Starlike and Convex Properties for Hypergeometric Functions
International Journal of Mathematics and Mathematical Sciences, 2008 The purpose of the present paper is to give some characterizations for a (Gaussian) hypergeometric function to be in various subclasses of starlike and convex functions. We also consider an integral operator related to the hypergeometric function.
Oh Sang Kwon, Nak Eun Cho
doaj +1 more source
A Generalised Hypergeometric Function [PDF]
Proceedings of the Edinburgh Mathematical Society, 1956 The hypergeometric function1F(a, b; c; z) is analytic in the domain |arg(−z)| < π, and, when |z| < 1, may be represented by the seriesWhen |z| = 1 in the domain |arg(−z)| <π, this series converges2 to F(a; b; c; z) if R(a+b−c) < 0 (integral values of a, b and c are excluded in the present paper).
openaire +1 more source
Celestial conformal blocks of massless scalars and analytic continuation of the Appell function F 1
Journal of High Energy PhysicsIn celestial conformal field theory (CCFT), the 4d massless scalars are represented by 2d conformal operators with conformal dimensions h = h ¯ $$ \overline{h} $$ = (1 + iλ)/2.
Wei Fan
doaj +1 more source
Fast calculation of scattering patterns using hypergeometric function algorithms. [PDF]
Sci Rep, 2023 Wagener M, Förster S.
europepmc +1 more source
Inequalities for hypergeometric functions [PDF]
Mathematics of Computation, 1976 The upper and lower bounds for the determinant of a dominant diagonal matrix have been used recently to obtain bounds on the classical orthogonal polynomials. Similar methods are used here on the hypergeometric functions of Gauss and of Kummer.
openaire +1 more source
Inequalities for some basic hypergeometric functions
Проблемы анализа, 2019 We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric functions with respect to the simultaneous shift of all its parameters.
Kalmykov S. I., Karp D. B.
doaj +1 more source