2 8 D ec 2 00 4 Lower - upper triangular decompositions , q = 0 limits , and p - adic interpretations of some q - hypergeometric orthogonal polynomials ∗ Tom
نویسنده
چکیده
For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relations which admit a dual system of orthogonal polynomials. For the q = 0 orthogonal limit functions we discuss interpretations on p-adic spaces. In the little 0-Jacobi case we also discuss product formulas.
منابع مشابه
8 N ov 2 00 4 Lower - upper triangular decompositions , q = 0 limits , and p - adic interpretations of some q - hypergeometric orthogonal polynomials Tom
For little q-Jacobi polynomials, q-Hahn polynomials and big q-Jacobi polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as decompositions into a lower triangular matrix times upper triangular matrix. We develop a general theory of such decompositions rela...
متن کاملdecompositions , q = 0 limits , and p - adic interpretations of some q - hypergeometric orthogonal polynomials
For little q-Jacobi polynomials, q-Hahn polynomials and big q-Jacobi polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as decompositions into a lower triangular matrix times upper triangular matrix. We develop a general theory of such decompositions rela...
متن کاملLU factorizations, q = 0 limits, and p-adic interpretations of some q-hypergeometric orthogonal polynomials
For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relation...
متن کاملM ar 1 99 4 q - Special Functions , A Tutorial TOM
A tutorial introduction is given to q-special functions and to q-analogues of the classical orthogonal polynomials, up to the level of Askey-Wilson polynomials. 0. Introduction It is the purpose of this paper to give a tutorial introduction to q-hypergeometric functions and to orthogonal polynomials expressible in terms of such functions. An earlier version of this paper was written for an inte...
متن کامل2 3 D ec 1 99 9 THE ASKEY - WILSON FUNCTION TRANSFORM SCHEME
In this paper we present an addition to Askey’s scheme of q-hypergeometric orthogonal polynomials involving classes of q-special functions which do not consist of polynomials only. The special functions are q-analogues of the Jacobi and Bessel function. The generalised orthogonality relations and the second order q-difference equations for these families are given. Limit transitions between the...
متن کامل