Certain hypergeometric series related to the root system $BC$

Elliptic Hypergeometric Series on Root Systems

We derive a number of summation and transformation formulas for elliptic hypergeometric series on the root systems An, Cn and Dn. In the special cases of classical and q-series, our approach leads to new elementary proofs of the corresponding identities.

An Analytic Method for Convergence Acceleration of Certain Hypergeometric Series

A method is presented for convergence acceleration of the generalized hypergeometric series 3F2 with the argument ±1 , using analytic properties of their terms. Iterated transformation of the series is performed analytically, which results in obtaining new fast converging expansions for some special functions and mathematical constants.

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

NEW TRANSFORMATIONS FOR ELLIPTIC HYPERGEOMETRIC SERIES ON THE ROOT SYSTEM An

Abstract. Recently, Kajihara gave a Bailey-type transformation relating basic hypergeometric series on the root system An, with different dimensions n. We give, with a new, elementary, proof, an elliptic analogue of this transformation. We also obtain further Bailey-type transformations as consequences of our result, some of which are new also in the case of basic and classical hypergeometric s...

On Bc Type Basic Hypergeometric Orthogonal Polynomials

Abstract. The five parameter family of multivariable Askey-Wilson polynomials is studied with four parameters generically complex. The multivariable Askey-Wilson polynomials form an orthogonal system with respect to an explicit (in general complex) measure. A partially discrete orthogonality measure is obtained by shifting the contour to the torus while picking up residues. A parameter domain i...