Divisibility results concerning truncated hypergeometric series

Divisibility Properties of Hypergeometric Polynomials

In this paper we give effective upper bounds for the degree k of divisors (over Q) of hypergeometric polynomials defined by n

On Divisibility concerning Binomial Coefficients

Binomial coefficients arise naturally in combinatorics. Recently the speaker initiated the study of certain divisibility properties of binomial coefficients, and products or sums of binomial coefficients. In this talk we introduce the speaker’s related results and various conjectures. The materials come from the author’s two preprints: 1. Z. W. Sun, Products and sums divisible by central binomi...

Certain Results on Hypergeometric Series for Meijer’s G-Functions

Truncated Hypergeometric Series Motivated by the Works of Slater and Verma

Motivated by the works of L.J. Slater and A. Verma, we have derived some results on truncated unilateral generalized hypergeometric series of positive unit argument subject to certain conditions in numerator and denominator parameters. The results presented here are presumably new.

Theta hypergeometric series

We formulate general principles of building hypergeometric type series from the Jacobi theta functions that generalize the plain and basic hy-pergeometric series. Single and multivariable elliptic hypergeometric series are considered in detail. A characterization theorem for a single variable totally elliptic hypergeometric series is proved.