Displaying similar documents to “Generating function and orthogonality property of a class of polynomials occurring in quantum mechanics”

A new exceptional polynomial for the integer transfinite diameter of [ 0 , 1 ]

Qiang Wu (2003)

Journal de théorie des nombres de Bordeaux

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Using refinement of an algorithm given by Habsieger and Salvy to find integer polynomials with smallest sup norm on [0, 1] we extend their table of polynomials up to degree 100. For the degree 95 we find a new exceptionnal polynomial which has complex roots. Our method uses generalized Müntz-Legendre polynomials. We improve slightly the upper bound for the integer transfinite diameter of [0, 1] and give elementary proofs of lower bounds for the exponents of some critical polynomials. ...

Linearization of Arbitrary products of classical orthogonal polynomials

Mahouton Hounkonnou, Said Belmehdi, André Ronveaux (2000)

Applicationes Mathematicae

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A procedure is proposed in order to expand w = ∏ j = 1 N P i j ( x ) = ∑ k = 0 M L k P k ( x ) where P i ( x ) belongs to aclassical orthogonal polynomial sequence (Jacobi, Bessel, Laguerre and Hermite) ( M = ∑ j = 1 N i j ). We first derive a linear differential equation of order 2 N satisfied by w, fromwhich we deduce a recurrence relation in k for the linearizationcoefficients L k . We develop in detail the two cases [ P i ( x ) ] N , P i ( x ) P j ( x ) P k ( x ) and give the recurrencerelation in some cases (N=3,4), when the polynomials P i ( x ) are monic Hermite orthogonal polynomials.