Some More Semi-finite Forms of Bilateral Basic Hypergeometric Series
نویسنده
چکیده
We prove some new semi-finite forms of bilateral basic hypergeometric series. One of them yields in a direct limit Bailey’s celebrated 6ψ6 summation formula, answering a question recently raised by Chen and Fu (Semi-Finite Forms of Bilateral Basic Hypergeometric Series, Proc. Amer. Math. Soc., to appear).
منابع مشابه
J an 2 00 7 On the Bilateral Series 2 ψ 2
It is well known that many bilateral basic hypergeometric identities can be derived from unilateral identities. Using Cauchy’s method [5, 15, 20, 21] one may obtain bilateral basic hypergeometric identities from terminating unilateral identities. Starting with nonterminating unilateral basic hypergeometric series, Chen and Fu [8] developed a method to construct semi-finite forms by shifting the...
متن کاملSemi-Finite Forms of Bilateral Basic Hypergeometric Series
Abstract. We show that several classical bilateral summation and transformation formulas have semi-finite forms. We obtain these semi-finite forms from unilateral summation and transformation formulas. Our method can be applied to derive Ramanujan’s 1ψ1 summation, Bailey’s 2ψ2 transformations, and Bailey’s 6ψ6 summation. Corresponding Author: William Y. C. Chen, Email: [email protected] AMS Cl...
متن کاملElementary Derivations of Identities for Bilateral Basic Hypergeometric Series
We give elementary derivations of several classical and some new summation and transformation formulae for bilateral basic hypergeometric series. For purpose of motivation, we review our previous simple proof (“A simple proof of Bailey’s very-well-poised 6ψ6 summation”, Proc. Amer. Math. Soc., to appear) of Bailey’s very-well-poised 6ψ6 summation. Using a similar but different method, we now gi...
متن کاملInversion of Bilateral Basic Hypergeometric Series
We present a new matrix inverse with applications in the theory of bilateral basic hypergeometric series. Our matrix inversion result is directly extracted from an instance of Bailey’s very-well-poised 6ψ6 summation theorem, and involves two infinite matrices which are not lower-triangular. We combine our bilateral matrix inverse with known basic hypergeometric summation theorems to derive, via...
متن کاملNoncommutative Extensions of Ramanujan’s 1ψ1 Summation ∗
Using functional equations, we derive noncommutative extensions of Ramanujan's 1 ψ 1 summation. 1. Introduction. Hypergeometric series with noncommutative parameters and argument, in the special case involving square matrices, have been the subject of recent study, see e.g. the papers by Duval and Ovsienko [DO], Grünbaum [G], Tirao [T], and some of the references mentioned therein. Of course, t...
متن کامل