Some properties of \(q\)-biorthogonal polynomials
\textit{W. A. Al-Salam} and \textit{A. Verma} [Pac. J. Math. 108, 1--7 (1983; Zbl 0471.33009)] constructed some \(q\)-extensions of a pair of biorthogonal polynomials \(Y_n^\alpha(x;k)\) and \(Z^\alpha_n(x;k)\) \((\alpha>-1;k\in N)\), which they called the \(q\)-Konhauser polynomials. \textit{V. K. Jain} and \textit{H. M. Srivastava} [J. Math. Anal. Appl. 166, 331--344 (1992; Zbl 0752.33008)], derived linear and bilinear generating functions for one of these \(q\)-Konhauser polynomials and also suggested an alternative pair of \(q\)-Konhauser biorthonal polynomials. In this paper a systematic investigation of the general family of \(q\)-biorthogonal polynomials is presented and several interesting properties and results are derived for these \(q\)-polynomials.
scientific article; zbMATH DE number 5125942
scientific article