In 1992, Koepf [J. Symb. Comp. 13 (1992) 581] introduced an algorithm for computing a Formal Power Series of a given function using generalized hypergeometric series and a recurrence equation of hypergeometric type. The main aim of this paper is to develop a new algorithm for computing exact power series solutions of second order linear differential equations with polynomial coefficients, near ...

Abstract: The generalized hypergeometric coherent states (GHCSs) have been introduced by Appl and Schiller [1]. In the present paper we have extended some considerations about GHCSs to the mixed (thermal) states and applied, particularly, to the case of pseudoharmonic oscillator (PHO). The Husimi’s Q distribution function and the diagonal P distribution function, in the GHCSs representation, ha...

Using the Wright’s generalized hypergeometric function, we investigate a class W (q, s;A,B, λ) of analytic functions with negative coefficients. We derive many results for the modified Hadamard product of functions belonging to the class W (q, s;A,B, λ). Moreover, we generalize some of the distortion theorems to the classical fractional integrals and derivatives and the Saigo (hypergeometric) o...

We survey several results on A-hypergeometric systems of linear partial differential equations introduced by Gelfand, Kapranov and Zelevinsky in the case of integer (and thus resonant) parameters, in particular, those differential systems related to sparse systems of polynomial equations. We also study in particular the case of A-hypergeometric systems for which kerA has rank 1. This allows us ...

Recently, the generalized hypergeometric function is extended by utilizing the Beta function. Based on this type of function, we introduce a new operator in the open unit disk. The present article investigates some subordination and superordination results for certain normalized analytic functions in the open unit disk, which are acted upon by the generalized Noor integral operator. Some of out...