Related papers: A formula for the nonsymmetric Opdam's hypergeomet…
The Heckman-Opdam hypergeometric functions of type BC extend classical Jacobi functions in one variable and include the spherical functions of non-compact Grassmann manifolds over the real, complex or quaternionic numbers. There are various…
We introduce new kind of $p$-adic hypergeometric functions. We show these functions satisfy congruence relations, so they are convergent functions. And we show that there is a transformation formula between our new $p$-adic hypergeometric…
Given any ${\bf{a}}: = \left( {a_1 ,a_2 , \ldots ,a_n } \right)$ and ${\bf{b}}: = \left( {b_1 ,b_2 , \ldots ,b_n } \right)$ in $\mathbb{R}^n$. The $\textbf{n}$-fold convex function defined on $\left[ {{\bf{a}},{\bf{b}}} \right]$,…
The main object of this work is to show how some rather elementary techniques based upon certain inverse pairs of symbolic operators would lead us easily to several decomposition formulas associated with confluent hypergeometric functions…
We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each…
We consider a certain definite integral involving the product of two classical hypergeometric functions having complicated arguments. We show in this paper the surprising fact that this integral does not depend on the parameters of the…
The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically…
Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain…
In this paper, we define a new type multivariable hypergeometric function. Then, we obtain some generating functions for these functions. Furthermore, we derive various families of multilinear and multilateral generating functions for these…
In this paper a double integral containing two Gaussian hypergeometric functions is discussed. The integral is not found in the literature and a direct computation is not (yet) possible. Therefore, a complete different integral is computed…
We calculate some finite and infinite sums containing the digamma function in closed-form. For this purpose, we differentiate selected reduction formulas of the hypergeometric function with respect to the parameters applying some derivative…
We show a connection formula for the $q$-confluent hypergeometric functions ${}_2\varphi_1(a,b;0;q,x)$. Combining our connection formula with Zhang's connection formula for ${}_2\varphi_0(a,b;-;q,x)$, we obtain the connection formula for…
In this brief note, we show how to apply Kummer's and other quadratic transformation formulas for Gauss' and generalized hypergeometric functions in order to obtain transformation and summation formulas for series with harmonic numbers that…
Starting from the hyperoctahedral multivariate hypergeometric function of Heckman and Opdam (associated with the $BC_n$ root system), we arrive -- via partial confluent limits in the sense of Oshima and Shimeno -- at solutions of the…
In this paper, The author introduces the concepts of the GA-s-convex functions in the first sense and second sense and establishes some integral inequalities of Hermite-Hadamard type related to the GA-s-convex functions.
We generalize the known constructions of A-hypergeometric functions. In particular, we show that periods of middle dimension on affine or projective complex algebraic varieties are A-hypergeometric functions of coefficients of polynomial…
The two most commonly used hypergeometric functions are the confluent hypergeometric function and the Gauss hypergeometric function. We review the available techniques for accurate, fast, and reliable computation of these two hypergeometric…
We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
This paper collects some important formulas on hyperbolic volume. To determine concrete values of volume function is a very hard question requiring the knowledge of various methods. Our goal to give a non-elementary integral on the volume…