Summation, transformation, and expansion formulas for multibasic theta hypergeometric series

Details Summation, transformation, and expansion formulas for multibasic theta hypergeometric series Summation, transformation, and expansion formulas for multibasic theta hypergeometric series

2005-05-11

arxiv.org/abs/math/0505215v1

Adv. Stud. Contemp. Math. (Kyungshang) 11 (2005), no. 1, 67-84

Mathematics

Classical Analysis and ODEs

18 pages; for the proceedings of the workshop "Elliptic Integrable Systems" (RIMS, Kyoto, November 8-11, 2004), special volume

Scientific paper

After reviewing some fundamental facts from the theory of theta hypergeometric series we derive, using indefinite summation, several summation, transformation, and expansion formulas for multibasic theta hypergeometric series. Some of the identities presented here generalize corresponding formulas given in Chapter 11 of the Gasper and Rahman book [Basic hypergeometric series, 2nd ed., Encyclopedia of Mathematics And Its Applications 96, Cambridge University Press, Cambridge, 2004].

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