Abstract

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 quadratic, cubic, and quartic transformations. Furthermore, we put forward the so-called ( R , S ) -type transformation with arbitrary degree to unify such multibasic transformations. A special ( 3 , 3 ) -type transformation and its example are presented.

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