2016/01/29 by H. S. Cohl, Cohl, H. S., R. S. Costas-Santos +3
Mathematics · #33C45 #42C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:33C45 #msc:42C05
paper · pdf · doi:10.48550/arxiv.1601.08178
12 pages, 2 figures
arxiv created 2016/01/29 · arxiv updated 2016/02/01
In this contribution, we study the orthogonality conditions satisfied by Al-Salam-Carlitz polynomials U(a)n(x;q) when the parameters a and q are not necessarily real nor `classical', i.e., the linear functional \bf u with respect to such polynomial sequence is quasi-definite and not positive definite. We establish orthogonality on a simple contour in the complex plane which depends on the parameters. In all cases we show that the orthogonality conditions characterize the Al-Salam-Carlitz polynomials Un(a)(x;q) of degree n up to a constant factor. We also obtain a generalization of the unique generating function for these polynomials.