Gosper s summation algorithm nds a hypergeometric closed form of an inde nite sum of hyperge ometric terms if such a closed form exists We generalize his algorithm to the case when the terms are simultaneously hypergeometric and multibasic q hypergeometric We also provide algorithms for computing hypergeometric canonical forms of rational functions and for nding polynomial solutions of recurren...

We study a 3–parametric family of stochastic point processes on the one–dimensional lattice originated from a remarkable family of representations of the infinite symmetric group. We prove that the correlation functions of the processes are given by determinantal formulas with a certain kernel. The kernel can be expressed through the Gauss hypergeometric function; we call it the hypergeometric ...

We describe a multiplicative normal form for rational functions which exhibits the shift structure of the factors, and investigate its properties. On the basis of this form we propose an algorithm which, given a rational function R, extracts a rational part F from the product of consecutive values of R: ∏n−1 k=n0 R(k) = F (n) ∏n−1 k=n0 V (k) where the numerator and denominator of the rational f...

The structure of multivariate hypergeometric terms is studied. This leads to a proof of (a special case of) a conjecture formulated by Wilf and Zeilberger in 1992. A function u(n1, . . . , nd) with values in a field K is called a hypergeometric term if there exist rational functions Ri ∈ K(n1, . . . , nd), i = 1, . . . , d, such that u is solution of a system of d firstorder recurrences Si · u ...

In this paper, the Stein-Chen method and the w-function associated with the negative hypergeometric random variable are used to give a result of the Poisson approximation to the negative hypergeometric distribution in terms of the total variation distance. Some numerical examples are presented to illustrate the result obtained. 2010 Mathematics Subject Classification: 60F05

Given the hypergeometric function F (a, b; c; z) = ∞ P n=0 (a)n(b)n (c)n(1)n zn, we place conditions on a, b and c to guarante that zpF (a, b; c; z) will be in various subclasses of p-valent starlike and p-valent convex functions. Operators related to the hypergeometric function are also examined.

The purpose of the present article is to introduce several new subclasses of meromorphic functions defined by using the multiplier transformation and hypergeometric function and investigate various inclusion relationships for these subclasses. Some interesting applications involving a certain class of hypergeometric functions are also considered. 2000 Mathematics Subject Classification: 30C45.

By using the integral representation of Gaussian hypergeometric function, we obtain Hilbert type inequalities with some fractional kernels and non-conjugate parameters. Such inequalities include the constant factors expressed in terms of hypergeometric functions. Further, we obtain the best possible constants for some general cases, in conjugate case.