By introducing multiparameter generalization of Bailey pair,the purpose of this paper is to find a number of new Rogers-Ramanujan-Bailey type identities.
The purpose of this paper is to establish several transformation formulae for bivariate basic hypergeometric series by means of series rearrangement technique. From these transformations, some interesting summation formulae are obtained.
Suppose R is a principal ideal ring, R^＊ is a multiplicative group which is composed of all reversible elements in R, and Mn（R）, GL（n,R）, SL（n,R） are denoted by,Mn（R）={A=（aij）n×n｜aij∈R,i,j=1,2…,n},GL（n,R）={g｜g∈Mn（R）,det g∈R^＊},SL（n,R）={g∈GL（n,R）｜det g=1},SL（n,R）≤G≤GL（n,R）（n≥3）,respectively,then basing on these facts, this paper mainly focus on discussing all extended groups of Gr={（O D^A B）∈G｜A∈GL（r,R）,（1≤r〈n）}in G when R is a principal ideal ring.
By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the infinite series Σr≥m tn＋r/（n＋rr）.
The purpose of this paper is to establish some identities with products of qHermite polynomials, q-ultraspherical polynomials and reciprocals of q-binomial coefficients.
A conjecture posed by Melham for Un2k+Un+12k in [2] is considered in this article.Several positive results on Vn+s2k +(-1)k(p2-4)kUn2k and V n2k+(-1)k(p2-4)kUn+s2k are achieved which generalize existed results on V n+12-(p2-4)Un2 and Vn2-(p2-4)Un+12.
