Related papers: Elliptic hypergeometric series on root systems
A multiple generalization of elliptic hypergeometric series is investigated and a duality transformation for multiple hypergeometric series is proposed. Our duality transformation obtained from an identity arising from the Cauchy…
Source identities are fundamental identities between multivariable special functions. We give a geometric derivation of rational and trigonometric source identities. We also give a systematic derivation and extension of various determinant…
A master formula of transformation formulas for bilinear sums of basic hypergeometric series is proposed. It is obtained from the author's previous results on a transformation formula for Milne's multivariate generalization of basic…
We give elementary proofs of the univariate elliptic beta integral with bases $|q|, |p|<1$ and its multiparameter generalizations to integrals on the $A_n$ and $C_n$ root systems. We prove also some new unit circle multiple elliptic beta…
In this brief note, we show how to apply Kummer's and other quadratic transformation formulas for Gauss' and generalized hypergeometric functions in order to obtain transformation and summation formulas for series with harmonic numbers that…
We study multivariable (bilateral) basic hypergeometric series associated with (type $A$) Macdonald polynomials. We derive several transformation and summation properties for such series including analogues of Heine's ${}_2\phi_1$…
We give a closed form for $quotients$ of truncated basic hypergeometric series where the base $q$ is evaluated at roots of unity.
We establish a determinant formula for the bilinear form associated with the elliptic hypergeometric integrals of type $BC_n$ by studying the structure of $q$-difference equations to be satisfied by them. The determinant formula is proved…
By means of inversion techniques and several known hypergeometric series identities, summation formulas for Fox-Wright function are explored. They give some new hypergeometric series identities when the parameters are specified.
We provide an alternate approach to obtaining expansion formulas on the lines of the well-poised Bailey lemma. We recover results due to Spiridonov and Warnaar and one new formula of this type. These formulas contain an arbitrary sequence…
We consider some new limits for the elliptic hypergeometric integrals on root systems. After the degeneration of elliptic beta integrals of type I and type II for root systems $A_n$ and $C_n$ to the hyperbolic hypergeometric integrals, we…
We prove a new Bailey-type transformation relating WP-Bailey pairs. We then use this transformation to derive a number of new 3- and 4-term transformation formulae between basic hypergeometric series.
We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided. As a byproduct new summation formulas…
In this article, we derive some identities for multilateral basic hypergeometric series associated to the root system A_n. First, we apply Ismail's argument to an A_n q-binomial theorem of Milne and derive a new A_n generalization of…
The general problem of the factorization of a basic hypergeometric series is presented and discussed. The case of the general $_2\psi_2$ series is examined in detail. Connections are found with the theory of basic hypergeometric series on…
We prove a summation formula for a bilateral series whose terms are products of two basic hypergeometric functions. In special cases, series of this type arise as matrix elements of quantum group representations.
We define a general class of (multiple) integrals of hypergeometric type associated with the Jacobi theta functions. These integrals are related to theta hypergeometric series through the residue calculus. In the one variable case, we get…
We define a hypergeometric function over finite fields which is an analogue of the classical generalized hypergeometric series. We prove that this function satisfies many transformation and summation formulas. Some of these results are…
By using the theory of the elliptic integrals a new method of summation is proposed for a certain class of series and their derivatives involving hyperbolic functions. It is based on the termwise differentiation of the series with respect…
By employing certain extended classical summation theorems, several surprising \pi and other formulae are displayed.