# Linearization of the product of orthogonal polynomials of a discrete variable

Saïd Belmehdi; Stanisław Lewanowicz; André Ronveaux

Applicationes Mathematicae (1997)

- Volume: 24, Issue: 4, page 445-455
- ISSN: 1233-7234

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topBelmehdi, Saïd, Lewanowicz, Stanisław, and Ronveaux, André. "Linearization of the product of orthogonal polynomials of a discrete variable." Applicationes Mathematicae 24.4 (1997): 445-455. <http://eudml.org/doc/219184>.

@article{Belmehdi1997,

abstract = {Let $P_k$ be any sequence of classical orthogonal polynomials of a discrete variable. We give explicitly a recurrence relation (in k) for the coefficients in $P_iP_j=\sum _kc(i,j,k)P_k$, in terms of the coefficients σ and τ of the Pearson equation satisfied by the weight function ϱ, and the coefficients of the three-term recurrence relation and of two structure relations obeyed by $P_k$.},

author = {Belmehdi, Saïd, Lewanowicz, Stanisław, Ronveaux, André},

journal = {Applicationes Mathematicae},

keywords = {linearization coefficients; classical orthogonal polynomials of a discrete variable; recurrence relations},

language = {eng},

number = {4},

pages = {445-455},

title = {Linearization of the product of orthogonal polynomials of a discrete variable},

url = {http://eudml.org/doc/219184},

volume = {24},

year = {1997},

}

TY - JOUR

AU - Belmehdi, Saïd

AU - Lewanowicz, Stanisław

AU - Ronveaux, André

TI - Linearization of the product of orthogonal polynomials of a discrete variable

JO - Applicationes Mathematicae

PY - 1997

VL - 24

IS - 4

SP - 445

EP - 455

AB - Let $P_k$ be any sequence of classical orthogonal polynomials of a discrete variable. We give explicitly a recurrence relation (in k) for the coefficients in $P_iP_j=\sum _kc(i,j,k)P_k$, in terms of the coefficients σ and τ of the Pearson equation satisfied by the weight function ϱ, and the coefficients of the three-term recurrence relation and of two structure relations obeyed by $P_k$.

LA - eng

KW - linearization coefficients; classical orthogonal polynomials of a discrete variable; recurrence relations

UR - http://eudml.org/doc/219184

ER -

## References

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- J. Letessier, A. Ronveaux and G. Valent, Fourth order difference equation for the associated Meixner and Charlier polynomials, J. Comput. Appl. Math. 71 (1996), 331-341. Zbl0856.33008
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- A. F. Nikiforov, S. K. Suslov and V. B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991. Zbl0743.33001
- A. Ronveaux, S. Belmehdi, E. Godoy and A. Zarzo, Recurrence relations approach for connection coefficients-Applications to classical discrete orthogonal polynomials, in: Symmetries and Integrability of Difference Equations, D. Levi, L. Vinet and P. Winternitz (eds.), Centre de Recherches Mathématiques, CRM Proc. and Lecture Notes Ser. 9, Amer. Math. Soc., Providence, 1996, 321-337. Zbl0862.33006

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