Connection formula of symmetric A-type Jackson integrals

Aomoto, Kazuhiko; Kato, Yoshifumi

doi:10.1215/s0012-7094-94-07406-1

Cited by 14 publications

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The method for proving the results in this paper is consistent with the concept introduced by Aomoto and Aomoto-Kato in the early 1990's in the series of papers [4,5,6,7,8,9,10,11,12]. Aomoto showed an isomorphism between a class of Jackson integrals of hypergeometric type, which he called the q-analog de Rham cohomology [4,5], and a class of theta functions, i.e., holomorphic functions possessing a quasi-periodicity [7,Theorem 1].…”

Section: Introductionsupporting

confidence: 65%

A bilateral extension of the $q$-Selberg integral

Ito

Forrester

2016

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

A multi-dimensional bilateral q-series extending the q-Selberg integral is studied using concepts of truncation, regularization and connection formulae. Following Aomoto's method, which involves regarding the q-series as a solution of a q-difference equation fixed by its asymptotic behavior, an infinite product evaluation is obtained. The q-difference equation is derived applying the shifted symmetric polynomials introduced by Knop and Sahi. As a special case of the infinite product formula, Askey-Evans's q-Selberg integral evaluation and its generalization by Tarasov-Varchenko and Stokman is reclaimed, and an explanation in the context of Aomoto's setting is thus provided.

show abstract

Section: Introductionsupporting

confidence: 65%

A bilateral extension of the $q$-Selberg integral

Ito

Forrester

2016

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…As already mentioned, the aim of this paper is to give an explanation for the formulae of product expression of these sums from a view-point of q-difference equations. The method for proving these results is consistent with the concepts introduced by Aomoto and Aomoto-Kato in the early 1990's in the series of papers [3,4,5,6,7,8,9,10]. Aomoto showed an isomorphism between a class of the Jackson integrals of hypergeometric type, which he called the q-analog de Rham cohomology [3,4], and a class of theta functions, i.e., holomorphic functions possessing a quasi-periodicity [6,Theorem 1].…”

Section: Introductionsupporting

confidence: 57%

The q-Dixon–Anderson integral and multi-dimensionalψ11summations

Ito

Forrester

2015

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

“…we use a modification of the method used by Aomoto [2] to evaluate the q-Selberg integral. There are two main steps.…”

Section: Normalization Integral For λ =mentioning

confidence: 99%

Multivariable Al-Salam & Carlitz Polynomials Associated with the TypeA q-Dunkl Kernel

Baker

Forrester

2000

Math. Nachr.

View full text Add to dashboard Cite

The Al-Salam & Carlitz polynomials are q-generalizations of the classical Hermite polynomials. Multivariable generalizations of these polynomials are introduced via a generating function involving a multivariable hypergeometric function which is the q-analogue of the type-A Dunkl integral kernel. An eigenoperator is established for these polynomials and this is used to prove orthogonality with respect to a certain Jackson integral inner product. This inner product is normalized by deriving a q-analogue of the Mehta integral, and the corresponding normalization of the multivariable Al-Salam & Carlitz polynomials is derived from a Pieri-type formula. Various other special properties of the polynomials are also presented, including their relationship to the shifted Macdonald polynomials and the big-q Jacobi polynomials.

show abstract

Connection formula of symmetric A-type Jackson integrals

Cited by 14 publications

References 9 publications

A bilateral extension of the $q$-Selberg integral

A bilateral extension of the $q$-Selberg integral

The q-Dixon–Anderson integral and multi-dimensionalψ11summations

Multivariable Al-Salam & Carlitz Polynomials Associated with the TypeA q-Dunkl Kernel

Contact Info

Product

Resources

About