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International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 10, Pages 673-689

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 Hindawi Publishing Corporation. 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.


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 (1μ)>0 in such a way that for μ=0 one has the well-known Jacobi polynomial sequence {Pˆn(α,α+1)(x)}, n0.