\(d\)-orthogonality of little \(q\)-Laguerre type polynomials
The authors introduce the \(L_{q}\) classical \(d\)-orthogonal polynomials of little \(q\)-Laguerre type, \(P_{n}(x,(\beta_{s})|q)\), \(s=0,\dots,d\) and \(\beta_{j}\), \(j=1,\dots,s\) are complex numbers such as \(\beta_{j}\neq 0,1,q^{-1}, q^{-2},\dots\) and study their properties. The obtained polynomials can be viewed as a q-analog of the d-orthogonal polynomials of Laguerre type, which were introduced by Y. Ben Cheikh and K. Douak, if we put \((q,s)=(1,d)\). Also, for \((d,s)=(1,0)\) the polynomials \(P_{n}(x,(\beta_{s})|q)\) give a new class of q-orthogonal polynomials and for \((d,s)=(1,1)\) they become the little q-Laguerre polynomials.
scientific article; zbMATH DE number 5969815
scientific article