Related papers: A formula for the nonsymmetric Opdam's hypergeomet…
We express explicitly the Heckman-Opdam hypergeometric function for the root system of type A with a certain degenerate parameter in terms of the Lauricella hypergeometric function.
We present an explicit difference equation for the Heckman-Opdam hypergeometric function associated with root systems. Via a confluent hypergeometric limit, an analogous difference equation is obtained for the class-one Whittaker function…
In this paper, we prove some Hermite-Hadamard type inequalities for operator geometrically convex functions for non-commutative operators. Keywords: Operator geometrically convex function, Hermite-Hadamard inequality.
Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing…
We define the adelic hypergeometric function of special Gaussian type by means of a tower of hypergeometric curves. This function takes values in an adelic completed group ring and interpolates all the hypergeometric functions of the same…
We prove an asymptotic formula for a special case of the Gauss hypergeometric function which arises in explicit formulas for moments of Maass form symmetric square L-functions. The resulting formula is uniform in several variables, which is…
This paper is concerned with two generalizations of the Hopf algebra of symmetric functions that have more or less recently appeared. The Hopf algebra of noncommutative symmetric functions and its dual, the Hopf algebra of quasisymmetric…
In this paper cycles for asymptotic solutions for Heckman-Opdam hypergeometric system of type $A_n$ are described. Cycles are enumerated by elements of symmetric group. Leading asymptotic and leading coefficient are calculated. Value of…
We study the Heckman-Opdam hypergeometric functions associated to a root system of type $BC$ and a multiplicity function which is allowed to assume some non-positive values (a standard multiplicity function). For such functions, we obtain…
A certain special function of the generalized hypergeometric variety is shown to fulfill a host of useful noncommutative identities.
We give a systematic and unified discussion of various classes of hypergeometric type equations: the hypergeometric equation, the confluent equation, the F_1 equation (equivalent to the Bessel equation), the Gegenbauer equation and the…
Many product formulas are known classically for generalized hypergeometric functions over the complex numbers. In this paper, we establish some analogous formulas for generalized hypergeometric functions over finite fields.
We introduce the symmetric (respectively, non-symmetric) $\tau_{-\ell}-$hypergeometric functions associated with a root system of type $BC$ as joint eigenfunctions of a commutative algebra of differential (respectively,…
The aim of this paper is to give, using some contiguous relations, the asymptotic behaviour of some linear combination of two symmetric contiguous hypergeometric functions, under some conditions of their parameters.
In this paper, we derive explicit product formulas and positive convolution structures for three continuous classes of Heckman-Opdam hypergeometric functions of type $BC$. For specific discrete series of multiplicities these hypergeometric…
We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.
The study is devoted to the construction of dynamical symmetry algebra of confluent hypergeometric function $_1F_1$ and $\Psi_2$-Humbert function and to derive some generating relations and reduction formulas for $_1F_1$ and $\Psi_2$…
We obtain a reflection formula for the Gaussian hypergeometric function of real symmetric matrix argument. We also show that this result extends to the Gaussian hypergeometric function defined over the symmetric cones, and even to…
We obtain symmetric joint eigenfunctions for the commuting PDOs associated to the hyperbolic Calogero-Moser N-particle system. The eigenfunctions are constructed via a recursion scheme, which leads to representations by multidimensional…
We give a new method to prove in a uniform and easy way various transformation formulas for Gauss hypergeometric functions. The key is Jacobi's canonical form of the hypergeometric differential equation. Analogy for $q$-hypergeometric…