Related papers: Hypergeometric Functions II (q-analogues)
We analyse the role of vertex operator algebra and 2d amplitudes from the point of view of the representation theory of infinite dimensional Lie algebras, MacMahon and Ruelle functions. A p-dimensional MacMahon function is the generating…
In this paper, an integral identity for twice differentiable functions is generalized. Then, by using convexity of |f''| or q-th power of |f''| and with the aid of power mean and Holder's inequalities we achieved some new results. We also…
With the help of some techniques based on certain inverse pairs of symbolic operators, the authors investigated several decomposition formulas associated with Srivastava's Hypergeometric functions of three variables. Some operator…
We give a definition of generalized hypergeometric functions over finite fields using modified Gauss sums, which enables us to find clear analogy with classical hypergeometric functions over the complex numbers. We study their fundamental…
With a large number of software tools dedicated to the visualisation and/or demonstration of properties of geometric constructions and also with the emerging of repositories of geometric constructions, there is a strong need of linking…
Generalized trigonometric functions and generalized hyperbolic functions can be converted to each other by the duality formulas previously discovered by the authors. In this paper, we apply the duality formulas to prove dual pairs of…
Infinite-dimensional, holomorphic functions have been studied in detail over the last several decades, due to their relevance to parametric differential equations and computational uncertainty quantification. The approximation of such…
We give a $q$-analogue of Howe duality associated to a pair $(\mf{g},G)$, where $\mf{g}$ is an orthosymplectic Lie superalgebra and $G=O_\ell, Sp_{2\ell}$. We define explicitly {commuting actions} of a quantized enveloping algebra of…
Several new $q$-supercongruences are obtained using transformation formulas for basic hypergeometric series, together with various techniques such as suitably combining terms, and creative microscoping, a method recently developed by the…
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.
In this paper, two new classes of convex functions as a generalization of convexity which is called (h-s)_{1,2}-convex functions are given. We also prove some Hadamard-type inequalities and applications to the special means are given.
This paper introduces a new generalized superfactorial function (referable to as $n^{th}$- degree superfactorial: $sf^{(n)}(x)$) and a generalized hyperfactorial function (referable to as $n^{th}$- degree hyperfactorial: $H^{(n)}(x)$), and…
In a recent paper [9], Ozdemir, Tunc and Akdemir defined two new classes of convex functions with which they proved some Hermite-Hadamard type inequalities. As an Open problem, they asked for conditions under which the composition of two…
We derive an explicit c-function expansion of a basic hypergeometric function associated to root systems. The basic hypergeometric function in question was constructed as explicit series expansion in symmetric Macdonald polynomials by…
We consider invariant hyperfunctions associated to automorphic forms on the upper half plane. We give two interpretations of the period function of Maass forms introduced by Lewis. The first interpretation shows that the period function…
Proposal for contribution to the quantum field theory section in "Encyclopedia of Mathematical Physics".
The A-hypergeometric system studied by I.M. Gelfand, M.I. Graev, A.V. Zelevinsky and the author, is defined for a set A of characters of an algebraic torus. In this paper we propose a generalization of the theory where the torus is replaced…
This is an expanded version of one of the Lectures in memory of Lars Ahlfors in Haifa in 1996. Some mistakes are corrected and references added. It contains a survey of his work on meromorphic functions and related topics written in…
By making use of some techniques based upon certain inverse new pairs of symbolic operators, the author investigate several decomposition formulas associated with Humbert hypergeometric functions $\Phi_1 $, $\Phi_2 $, $\Phi_3 $, $\Psi_1 $,…
We prove Macdonald-type deformations of a number of well-known classical branching rules by employing identities for elliptic hypergeometric integrals and series. We also propose some conjectural branching rules and allied conjectures…