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arXiv · 2309.02630

Three new $q$-Abel transformations and their applications

Jianan Xu·Xinrong Ma
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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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Jianan Xu, Xinrong Ma. 2023-09-06. Three new $q$-Abel transformations and their applications. https://arxiv.org/abs/2309.02630

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