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math.CV2013★ 6 cited
A bilateral extension of the -Selberg integral
Masahiko Ito, Peter J. Forrester
A multi-dimensional bilateral -series extending the -Selberg integral is studied using concepts of truncation, regularization and connection formulae. Following Aomoto's meth…
math.CV2013
Ramanujan's summation theorem --- perspective, announcement of bilateral -Dixon--Anderson and -Selberg integral extensions, and context
Masahiko Ito, Peter J. Forrester
The Ramanujan summation theorem in studied from the perspective of -Jackson integrals, -difference equations and connection formulas. This is an approach which has pr…
math.CV2013
The -Dixon--Anderson integral and multi-dimensional summations
Masahiko Ito, Peter J. Forrester
The Dixon--Anderson integral is a multi-dimensional integral evaluation fundamental to the theory of the Selberg integral. The summation is a bilateral generalization of th…