Factorization of the hypergeometric-type difference equation on the uniform lattice.
Fourier transform of .
Four-term recurrence relations for hypergeometric functions of the second order. II.
The recent work on four-term recurrence relations for the second order functions of hypergeometric type undertaken by the author is developed from a slightly different point of view also using generating functions. The direction of future prospects is indicated.
Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function
2000 Mathematics Subject Classification: 26A33, 33C45This paper refers to a fractional order generalization of the classical Jacobi polynomials. Rodrigues’ type representation formula of fractional order is considered. By means of the Riemann–Liouville operator of fractional calculus fractional Jacobi functions are defined, some of their properties are given and compared with the corresponding properties of the classical Jacobi polynomials. These functions appear as a special case of a fractional Gauss...
Functional Analysis, Orthogonal Polynomials And A Theorem Of Markov.
Gauss-Lobatto formulae and extremal problems with polynomials.
Gegenbauer matrix polynomials and second order matrix differential equations.
Generalizations of the Bernoulli and Appell polynomials.
Generalizations of the classical Chebyshev polynomials to polynomials in two variables
Generalized Hermite Polynomials
Generalized Krawtchouk polynomials: New properties
Orthogonality conditions and recurrence relations are presented for generalized Krawtchouk polynomials. Coefficients are evaluated for the expansion of an arbitrary polynomial in terms of these polynomials and certain special values for generalized Krawtchouk polynomials are obtained. Summations of some of these polynomials and of certain products are also considered.
Generating function and orthogonality property of a class of polynomials occurring in quantum mechanics
Generating functions and special functions.
Generating functions for certain q-orthogonal polynomials.
Generating functions for Jacobi and Laguerre polynomials
Generating functions on extended Jacobi polynomials from Lie group view point.
Generating functions play a large role in the study of special functions. The present paper deals with the derivation of some novel generating functions of extended Jacobi polynomials by the application of [the] group-theoretic method introduced by Louis Weisner. In fact, by suitably interpreting the index (n) and the parameter (β) of the polynomial under consideration we define four linear partial differential operators and on showing that they generate a Lie-algebra, we obtain a new generating...
Generating new classes of orthogonal polynomials.
Generating some semiclassical orthogonal polynomials.
Hardy and Cowling-Price theorems for a Cherednik type operator on the real line
This paper is aimed to establish Hardy and Cowling-Price type theorems for the Fourier transform tied to a generalized Cherednik operator on the real line.
Hardy-type inequalities for Hermite expansions.