165 research outputs found
General -series transformations based on Abel's lemma on summation by parts and their applications
In this paper, we establish three new and general transformations with
sixteen parameters and bases via Abel's lemma on summation by parts. As
applications, we set up a lot of new transformations of basic hypergeometric
series. Among include some new results of Gasper and Rahman's quadratic, cubic,
and quartic transformations. Furthermore, we put forward the so-called
-type transformation with arbitrary degree to unify such multibasic
transformations. Some special -type transformations are presented
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