Structure relations for the bivariate big q-Jacobi polynomials

摘要

We give structure relations for the orthogonal polynomials in two variables, defined by Lewanowicz and Woźny [S. Lewanowicz, P. Woźny, J. Comput. Appl. Math. 233 (2010) 1554–1561]Pn,k(x,y;a,b,c,d;q)≔Pn-k(y;a,bcq2k+1,dqk;q)ykdq/y;qkPkx/y;c,b,d/y;q(n⩾0;k=0,1,…,n)where q∈(0,1),0