Geodesic
Riordan arrays, Sheffer sequences and "orthogonal" polynomials
Journal of integer sequences, Tome 11 (2008) no. 5.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Riordan group concepts are combined with the basic properties of convolution families of polynomials and Sheffer sequences, to establish a duality law, canonical forms $\rho(n,m)={n\choose m}c^mF_{n-m}(m),\ c\neq0,$ and extensions $\rho(x,x-k)=(-1)^kx^{\underline{k+1}}c^{x-k}F_k(x)$, where the $F_k(x)$ are polynomials in $x$, holding for each $\rho(n,m)$ in a Riordan array. Examples $\rho(n,m)={n\choose m}S_k(x)$ are given, in which the $S_k(x)$ are "orthogonal" polynomials currently found in mathematical physics and combinatorial analysis.
Classification : 05A19, 05A15
Keywords: riordan group, convolution polynomials, polynomial extensions, Sheffer sequences, orthogonal polynomials 
@article{JIS_2008__11_5_a5,
     author = {Della Riccia, Giacomo},
     title = {Riordan arrays, {Sheffer} sequences and "orthogonal" polynomials},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {11},
     number = {5},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2008__11_5_a5/}
}
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Della Riccia, Giacomo. Riordan arrays, Sheffer sequences and "orthogonal" polynomials. Journal of integer sequences, Tome 11 (2008) no. 5. http://geodesic.mathdoc.fr/item/JIS_2008__11_5_a5/