@misc{FoupouagnigniRonveauxHounkonnou, author = {Foupouagnigni, Mama and Ronveaux, Andre and Hounkonnou, Mahouton Norbert}, title = {The Fourth-Order Difference Equation Satisfied by the Associated Orthogonal Polynomials of the Delta-Laguerre-HahnClass}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3409}, number = {SC-97-71}, abstract = {Starting from the \$ D_{ \omega}\$-Riccati Difference equation satisfied by the Stieltjes function of a linear functional, we work out an algorithm which enables us to write the unique fourth-order difference equation satisfied by the associated of any integer order of orthogonal polynomials of the \$ \Delta\$-Laguerre-Hahn class. Moreover, in classical situations (Meixner, Charlier, Kravtchouk and Hahn), we give explicitely these difference equations; and from Hahn difference equation, we recover by limit process the difference equations satisfied by the associated of classical discrete orthogonal polynomials and differential equations satisfied by the associated of classical continuous orthogonal polynomials.}, language = {en} } @misc{FoupouagnigniKoepfRonveaux, author = {Foupouagnigni, Mama and Koepf, Wolfram and Ronveaux, Andre}, title = {Fourth Order Difference Equation for the Associated Classical Discrete Orthogonal Polynomials}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3419}, number = {SC-97-72}, abstract = {We derive the fourth order difference equation satisfied by the associated of order \$\;r\;\$ of the classical orthogonal polynomials of a discrete variable.\\The coefficients of this equation are given in terms of the polynomials \$\; \sigma\;\$ and \$\;\tau\;\$ which appear in the discrete Pearson equation \$\;\;\Delta(\sigma\;\rho)=\tau\;\rho\;\;\$ defining the weight \$\;\rho(x)\;\$ of the classical discrete orthogonal polynomials.}, language = {en} } @misc{FoupouagnigniRonveauxKoepf, author = {Foupouagnigni, Mama and Ronveaux, Andre and Koepf, Wolfram}, title = {Fourth-Order q-Difference Equation for the First Associated of the q-Classical Orthogonal Polynomials}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3490}, number = {SC-98-06}, abstract = {We derive the fourth order \$q\$-difference equation satisfied by the first associated of the \$q\$-classical orthogonal polynomials. The coefficients of this equation are given in terms of the polynomials \$\; \sigma\;\$ and \$\;\tau\;\$ which appear in the \$q\$-Pearson difference equation \$\;\; D_q(\sigma\,\rho)=\tau\,\rho\;\$ defining the weight \$\rho\$ of the \$q\$-classical orthogonal polynomials inside the \$q\$-Hahn tableau.}, language = {en} }