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We give integral representations for multiple Hermite and multiple Laguerre polynomials of both type I and II. We also show how these are connected with double integral representations of certain kernels from random matrix theory.

Integral Representations of Functional Series with Members Containing Jacobi Polynomials

Jankov, Dragana, Pogany, Tibor K. (2012)

Mathematica Balkanica New Series

MSC 2010: Primary 33C45, 40A30; Secondary 26D07, 40C10In this article we establish a double definite integral representation, and two other indefinite integral expressions for a functional series and its derivative with members containing Jacobi polynomials.

Integrals involving Gegenbauer and Hermite polynomials on the imaginary axis.

C. Berg (1990)

Aequationes mathematicae

Integrals involving Hermite polynomials, generalized hypergeometric series and Fox's H-function, and Fourier-Hermite series for products of generalized hypergeometric functions

Sadhana Mishra (1991)

Annales Polonici Mathematici

We evaluate an integral involving an Hermite polynomial, a generalized hypergeometric series and Fox's H-function, and employ it to evaluate a double integral involving Hermite polynomials, generalized hypergeometric series and the H-function. We further utilize the integral to establish a Fourier-Hermite expansion and a double Fourier-Hermite expansion for products of generalized hypergeometric functions.

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Inequalities and identities for ... .

Inequalities for Laguerre functions.

Inequalities for the smallest zeros of Laguerre polynomials and their $q$ -analogues.

Integrability Theorems For Jacobi Series

Integral representation of orthogonal exponential polynomials

Integral representations for multiple Hermite and multiple Laguerre polynomials

Integral Representations of Functional Series with Members Containing Jacobi Polynomials

Integrals involving Gegenbauer and Hermite polynomials on the imaginary axis.

Integrals involving Hermite polynomials, generalized hypergeometric series and Fox's H-function, and Fourier-Hermite series for products of generalized hypergeometric functions

Interpolatorische Kubatorformeln und reelle Ideale.

Irrationality measures of $log 2$ and $π / \sqrt{3}$ .

Itération des polynômes et propriétés d'orthogonalité

Iterative square roots of Cebysev polynomials.

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