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This paper is devoted to the study of matrix elements of irreducible representations of the enveloping deformed Heisenberg algebra with reflection, motivated by recurrence relations satisfied by hypergeometric functions. It is shown that the matrix elements of a suitable operator given as a product of exponential functions are expressed in terms of $d$ -orthogonal polynomials, which are reduced to the orthogonal Meixner polynomials when $d = 1$ . The underlying algebraic framework allowed a systematic derivation...

Derivation of the Hille-Hardy type formulae and operational methods

Giuseppe Dattoli (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The Hille-Hardy formula is a bilinear generating function, involving products of Laguerre polynomials. We use the point of view, developed in previous publications, to propose an operational method which allows a fairly direct derivation of this kind of formulae.

Derivatives of orthonormal polynomials and coefficients of Hermite-Fejér interpolation polynomials with exponential-type weights.

Jung, H.S., Sakai, R. (2010)

Journal of Inequalities and Applications [electronic only]

Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials: the discrete case.

Ledoux, M. (2005)

Electronic Journal of Probability [electronic only]

Discrepancy convergence for the Drunkard's walk on the sphere.

Su, Francis Edward (2001)

Electronic Journal of Probability [electronic only]

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Displaying 101 – 120 of 462

Construction of a recurrence relation of the lowest order for coefficients of the Gegenbauer series

Construction of the lowest-order recurrence relation for the Jacobi coefficients

Continuité et différentiabilité des translations dans un espace Gaussien.

Continuous symmetrized Sobolev inner products of order $N$ . II.

Contributions to the theory of Hermitian series. III: Mean values.

Convergence of Padé approximants for a q-hypergeometric series (Wynn's Power Series III).

Convergence of Padé approximants for a q-hypergeometric series (Wynn's Power Series III). (Summary).

Convergence of Padé approximants for a q-hypergeometric series (Wynn's Power Series I). (Summary).

Convergence of Padé approximations for a q-hypergeometric series (Wynn's Power Series I).

Creation and annihilation operators for orthogonal polynomials of continuous and discrete variables.

Deformed Heisenberg algebra with reflection and $d$ -orthogonal polynomials

Derivation of the Hille-Hardy type formulae and operational methods

Derivatives of orthonormal polynomials and coefficients of Hermite-Fejér interpolation polynomials with exponential-type weights.

Development in series of orthogonal polynomials with applications in optimization.

Développements des distributions en séries de fonctions orthogonales. Séries de Legendre et de Laguerre

Die Laguerre-Pinney-Transformation.

Die Polynomlösungen spezieller partieller Differentialgleichungen.

Die Transformationsfunktion für eine Differentialgleichung zweiter Ordnung

Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials: the discrete case.

Discrepancy convergence for the Drunkard's walk on the sphere.

Currently displaying 101 – 120 of 462