An orthogonal polynomial coefficient formula for the Hankel transform

2011/03/30 by Paul Barry, Barry, Paul
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1103.5948

10 pages

arxiv created 2011/03/30 · arxiv updated 2011/03/31

Abstract

We give an explicit formula for the Hankel transform of a regular sequence in terms of the coefficients of the associated orthogonal polynomials and the sequence itself. We apply this formula to some sequences of combinatorial interest, deriving interesting combinatorial identities by this means. Further insight is also gained into the structure of the Hankel transform of a sequence.

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