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Vol.33 (2020) >

Authors :Ito, Masahiko
Takushi, Yamato
Issue Date :28-Dec-2020
Abstract :We provide a simpler proof for an infinite product expression of Gustafson’s q-beta integral of type G_2 with 4 parameters. We extend Gustafson’s q-integral to a q-hypergeometric integral of type G_2 with 6 parameters. Under a constraint of the parameters called the balancing condition, we obtain two explicit forms of q-difference equations satisfied by the q-hypergeometric integral of type G_2. Taking limit for a parameter, the q-hypergeometric integral of type G_2 degenerates to Gustafson’s q-integral, and one of two q-difference equations becomes that satisfied by Gustafson’s q-integral. Using this we consequently have an alternative proof for the infinite product of Gustafson’s q-beta integral again.
Type Local :紀要論文
ISSN :2434-6071
Publisher :Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus
URI :http://hdl.handle.net/20.500.12000/47630
Citation :Ryukyu Mathematical Journal Vol.33 p.1 -59
Appears in Collections:Vol.33 (2020)

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