@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{BoeingKoepf, author = {B{\"o}ing, Harald and Koepf, Wolfram}, title = {Algorithms for q-hypergeometric Summation in Computer Algebra}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3453}, number = {SC-98-02}, abstract = {In this paper we present a short description of \$q\$-analogues of Gosper's, Zeilberger's, Petkov\v{s}ek's and related algorithms. Furthermore we introduce our corresponding MAPLE implementations and show how they can be applied to prove or even derive identities associated with \$q\$-series.}, 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} }