TY - GEN A1 - Foupouagnigni, Mama A1 - Ronveaux, Andre A1 - Koepf, Wolfram T1 - Fourth-Order q-Difference Equation for the First Associated of the q-Classical Orthogonal Polynomials N2 - 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. T3 - ZIB-Report - SC-98-06 KW - q-Orthogonal polynomials KW - Fourth order q-difference equation Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3490 ER - TY - GEN A1 - Foupouagnigni, Mama A1 - Ronveaux, Andre A1 - Hounkonnou, Mahouton Norbert T1 - The Fourth-Order Difference Equation Satisfied by the Associated Orthogonal Polynomials of the Delta-Laguerre-HahnClass N2 - 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. T3 - ZIB-Report - SC-97-71 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3409 ER - TY - GEN A1 - Foupouagnigni, Mama A1 - Koepf, Wolfram A1 - Ronveaux, Andre T1 - Fourth Order Difference Equation for the Associated Classical Discrete Orthogonal Polynomials N2 - 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. T3 - ZIB-Report - SC-97-72 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3419 ER -