## Orthogonal expansions and their continuous analogues: proceedings of the conference held at Southern Illinois University, Edwardsville, April 27-29, 1967 |

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### Contents

An Outline of the History of Orthogonal Polynomials | 3 |

A Dual Convolution Structure for Jacobi Polynomials | 25 |

On the Associated Legendre Polynomials | 43 |

Copyright | |

11 other sections not shown

### Common terms and phrases

Abelian group absolutely continuous Amer analogue analytic assume asymptotic coefficients condition conjugate Consequently consider Const constant contains continuous function COROLLARY D. V. Widder defined degree denote differential equation estimate everywhere exists expansion fact finite fixed follows formula Fourier series Fourier-Stieltjes given half plane harmonic function harmonic measure Hence hn(x holds homogeneous hypothesis of Theorem implies inequality integer interval Jacobi polynomials kernel lacunary Laguerre polynomials Laguerre temperature Lebesgue measure Lemma lim sup linear martingale Mary Weiss Math middle half nonnegative nontangential limit obtain one-sided orthogonal polynomials orthonormal systems partial sums partition Poisson integral positive integer proof of Theorem prove Rademacher Rademacher function real axis real number result satisfies sequence sign regularity solution spherical harmonic subset Suppose Szego temperature functions théorème theory tion transform trigonometric series variable weight function zero Zygmund