Some new formulas involving Gamma q Functions
2007 (English)In: Rendiconti del Seminario Matematico della Universita di Padova, ISSN 0041-8994, Vol. 118, 159-188 p.Article in journal (Refereed) Published
In a recent paper we found some new results for q-functions of many variables with the aid of the T, function. The Heine notation reminding of the hypergeometric case was used throughout, and some relations between Gamma(q) functions were presented. This paper aims at giving the promised longer exposition of Gamma(q)- revealing also the connection between this and the Jacobi-theta functions which appear in context. We will give a slightly generalized definition of the Heine series with more general tilde operators. 4 q-summation formulas of Andrews will be given in the new notation. The close affinity to q-binomial coefficient formulas will be stressed by expressing the finite q-hypergeometric formulas, the canonical form, in two ways. Two further q-analogues of Kummer's 2F(1)(-1) formula will be given. An ancient q-analogue of the Euler reflection formula will be used for the proof of a special case of the Bailey-Daum summation formula, conjectured in the previous paper.
Place, publisher, year, edition, pages
2007. Vol. 118, 159-188 p.
IdentifiersURN: urn:nbn:se:uu:diva-112993ISI: 000252631800008OAI: oai:DiVA.org:uu-112993DiVA: diva2:289444