Showing papers by "Richard Askey published in 1971"

Jacobi polynomial expansions of Jacobi polynomials with non-negative coefficients

Abstract: The answers to many important questions in the harmonic analysis of orthogonal polynomials are known to depend on the determination of when formulas of the typesand their dualshold, where pn(x) and qn(x) are suitably normalized orthogonal polynomials or orthogonal polynomials multiplied by certain functions; e.g. e−pxLn(x).

Orthogonal Expansions with Positive Coefficients. II

Abstract: A sufficient condition is given for writing a set of orthogonal polynomials as a linear combination of a second set of orthogonal polynomials with nonnegative coefficients. Some inequalities for Pollaczek polynomials and associated ultraspherical polynomials follow from this result.