The fourth order difference equation for the Laguerre-Hahn polynomials orthogonal on special non-uniform lattices

Bangerezako, G
(2001) The Ramanujan Journal : an international journal devoted to areas of mathematics influenced by Ramanujan — Vol. 5, n° 2, p. 167-181 (2001)

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  • Bangerezako, G
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Abstract
We firstly establish the fourth order difference equation satisfied by the Laguerre-Hahn polynomials orthogonal on special non-uniform lattices in general case, secondly give it explicitly for the cases of polynomials r-associated to the classical polynomials orthogonal on linear, q-linear and q-nonlinear (Askey-Wilson) lattices, and thirdly give it "semi-explicitly" for the class one Laguerre-Hahn polynomials orthogonal on linear lattice.
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Bangerezako, G. (2001). The fourth order difference equation for the Laguerre-Hahn polynomials orthogonal on special non-uniform lattices. The Ramanujan Journal : an international journal devoted to areas of mathematics influenced by Ramanujan, 5(2), 167-181. https://doi.org/10.1023/A:1011487824004 (Original work published 2001)