Chebyshev polynomials, quadratic surds and a variation of Pascal's triangle
Résumé
Using Chebyshev polynomials
of both kinds, we construct rational fractions which are convergents
of the smallest root of $x^2-\alpha x+1$ for $\alpha=3,4,5,\dots$.
Some of the underlying identities suggest an identity involving binomial
coefficients which leads to a triangular array sharing many properties
with Pascal's triangle.
Domaines
Combinatoire [math.CO]| Origine | Fichiers produits par l'(les) auteur(s) |
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