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Three new $q$-Abel transformations and their applications (2309.02630v1)
Published 6 Sep 2023 in math.CO and math.CA
Abstract: In the present paper, we establish three special $q$-Abel transformation formulae of $q$-series via the use of Abel's lemma on summation by parts. As direct applications, we set up the corresponding $q$-contiguous relations for three kinds of truncated $q$-series. Several new transformations are consequently established.
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