Multivariable Appell functions show up in the work of Kac and Wakimoto in the computation of character formulas for certain s`(m, 1)∧ modules. Recently Bringmann and Ono showed that the character formulas for the s`(m, 1)∧ modules L(Λ(s)), where L(Λ(s)) is the irreducible s`(m, 1) ∧ module with highest weight Λ(s), can be seen as the “holomorphic parts” of certain nonholomorphic modular functio...

We investigate the structure of the Schrödinger algebra and its representations in a Fock space realized in terms of canonical Appell systems. Generalized coherent states are used in the construction of a Hilbert space of functions on which certain commuting elements act as self-adjoint operators. This yields a probabilistic interpretation of these operators as random variables. An interesting ...

This research is aimed to give a determinantal definition for the q-Appell polynomials and show some classical properties as well as find some interesting properties of the mentioned polynomials in the light of the new definition.

In this paper we resolve a question by Bringmann, Lovejoy, and Rolen on new vector-valued $U$-type function. We obtain an expression for corresponding family of Hecke-Appell-type sums in terms mixed mock modular forms; that is, express the sum Appell functions theta functions. This function appears from considering special polynomials related to generating partitions occurring Gordon generaliza...

We give a general approach to in nite dimensional non-Gaussian analysis which generalizes the work [KSWY95]. For given measure we construct a family of biorthogonal systems. We study their properties and their Gel'fand triples that they generate. As an example we consider the measures of Poisson type.

The high speed vibration of a flexible robotic arm compared to the low speed of software and hardware interface between the computer and experimental setup is one of the most important obstacles for measuring and control of such a systems. In this paper, a combination of using high speed digital to analog convertor (DAC) components on an electrical interface board and using National Instrument’...

Abstract. We find two-sided inequalities for the generalized hypergeometric function with positive parameters restricted by certain additional conditions. Our lower bounds are asymptotically precise at x = 0, while the upper bounds are either asymptotically precise or at least agree with q+1Fq((aq+1), (bq);−x) at x = ∞. Inequalities are derived as corollaries of a theorem asserting the monotony...

We study several properties of matrix variate beta type 3 distribution. We also derive probability density functions of the product of two independent random matrices when one of them is beta type 3. These densities are expressed in terms of Appell’s first hypergeometric function F1 and Humbert’s confluent hypergeometric functionΦ1 of matrix arguments. Further, a bimatrix variate generalization...

In the recent past one of the main concern of research in the field of Hypercomplex Function Theory in Clifford Algebras was the development of a variety of new tools for a deeper understanding about its true elementary roots in the Function Theory of one Complex Variable. Therefore the study of the space of monogenic (Clifford holomorphic) functions by its stratification via homogeneous monoge...