International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 10, Pages 673-689
doi:10.1155/S0161171200004671
An example of nonsymmetric semi-classical form of class s=1; generalization of a case of Jacobi sequence
Faculté des Sciences de Gabès, 6029 Route de Mednine Gabès, Tunisia
Received 24 February 2000
Copyright © 2000 Mohamed Jalel Atia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We give explicitly the recurrence coefficients of a nonsymmetric
semi-classical sequence of polynomials of class s=1. This
sequence generalizes the Jacobi polynomial sequence, that is, we
give a new orthogonal sequence {Pˆn(α,α+1)(x,μ)}, where μ is an arbitrary parameter with ℜ(1−μ)>0 in such a way that for μ=0 one has the well-known Jacobi polynomial sequence {Pˆn(α,α+1)(x)}, n≥0.