The q-Dixon-Anderson integral and multi-dimensional (1)psi(1) summations
Masahiko Ito, Peter J Forrester
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2015
The Dixon-Anderson integral is a multi-dimensional integral evaluation fundamental to the theory of the Selberg integral. The ψ11 summation is a bilateral generalization of the q-binomial theorem. It is shown that a q-generalization of the Dixon-Anderson integral, due to Evans, and multi-dimensional generalizations of the ψ11 summation, due to Milne and Gustafson, can be viewed as having a common origin in the theory of q-difference equations as expounded by Aomoto. Each is shown to be determined by a q-difference equation of rank 1, and a certain asymptotic behavior. In calculating the latter, essential use is made of the concepts of truncation, regularization and connection formulae.
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Awarded by Australian Research Council
Awarded by JSPS KAKENHI
This work was supported by the Australian Research Council (Grant DP110102317) and JSPS KAKENHI Grant Number 25400118.