The corresponding article has been published in
Can. J. Math. 41 (1989), 743-768.
Christian Krattenthaler
q-analogue of a two variable inverse pair of series with
applications to basic double hypergeometric series
Abstract.
We give a q-analogue of the following inverse pair of two-variable
formal power series: f0(z1,
z2)
= (z1/(1-z2),
z2/(1-z1))
and
F0(z1,z2)
= (z1(1-z2)/(1-z1 z2),
z2(1-z1)/(1-z1 z2)).
We use our
q-analogue to derive several double basic haypergeometric series
summations and transformations, some of them being already known,
most of them being new.
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