290 research outputs found
Multilateral inversion of A_r, C_r and D_r basic hypergeometric series
In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic
hypergeometric matrix inverse with applications to bilateral basic
hypergeometric series. This matrix inversion result was directly extracted from
an instance of Bailey's very-well-poised 6-psi-6 summation theorem, and
involves two infinite matrices which are not lower-triangular. The present
paper features three different multivariable generalizations of the above
result. These are extracted from Gustafson's A_r and C_r extensions and of the
author's recent A_r extension of Bailey's 6-psi-6 summation formula. By
combining these new multidimensional matrix inverses with A_r and D_r
extensions of Jackson's 8-phi-7 summation theorem three balanced
very-well-poised 8-psi-8 summation theorems associated with the root systems
A_r and C_r are derived.Comment: 24 page
On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series
Using Krattenthaler's operator method, we give a new proof of Warnaar's
recent elliptic extension of Krattenthaler's matrix inversion. Further, using a
theta function identity closely related to Warnaar's inversion, we derive
summation and transformation formulas for elliptic hypergeometric series of
Karlsson-Minton-type. A special case yields a particular summation that was
used by Warnaar to derive quadratic, cubic and quartic transformations for
elliptic hypergeometric series. Starting from another theta function identity,
we derive yet different summation and transformation formulas for elliptic
hypergeometric series of Karlsson-Minton-type. These latter identities seem
quite unusual and appear to be new already in the trigonometric (i.e., p=0)
case.Comment: 16 page
Hyperbolic beta integrals
Hyperbolic beta integrals are analogues of Euler's beta integral in which the
role of Euler's gamma function is taken over by Ruijsenaars' hyperbolic gamma
function. They may be viewed as -bibasic analogues of the
beta integral in which the two bases and are interrelated
by modular inversion, and they entail -analogues of the beta integral for
. The integrals under consideration are the hyperbolic analogues of the
Ramanujan integral, the Askey-Wilson integral and the Nassrallah-Rahman
integral. We show that the hyperbolic Nassrallah-Rahman integral is a formal
limit case of Spiridonov's elliptic Nassrallah-Rahman integral.Comment: 35 pages. Remarks and references to recent new developments are
added. To appear in Adv. Mat
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