Some remarks about q-Chebyshev polynomials and q-Catalan numbers and related results

2013/12/10 by Cigler, Johann
#Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1312.2767

Abstract

The moments of the Lucas polynomials and of the Chebyshev polynomials of the first kind are (multiples of) central binomial coefficients and the moments of the Fibonacci polynomials and of the Chebyshev polynomials of the second kind are Catalan numbers. In this survey paper we present some generalizations of these results together with various q-analogues.

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