A common formula for certain generalized Hankel transforms

2009/12/03 by Mario García-Armas, Mario Garcia-Armas, Garcia-Armas, Mario
Computer Science · Mathematics · #05A10 #11B65 #11C20 #15A15 #Combinatorics (math.CO) #Digital Filter Design and Implementation #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #math.CO #msc:05A10 #msc:11B65 #msc:11C20 #msc:15A15

paper · pdf · doi:10.48550/arxiv.0912.0684

10 pages. Not for publication

openalex publication_date 2009/12/03 · arxiv created 2012/03/23 · arxiv updated 2012/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the generalized Hankel transform of the family of sequences satisfying the recurrence relation a_n+1 = (α+ \fracβn+γ) a_n. We apply the obtained formula to several particular important sequences. Incidentally, we find a connection between some well known formulas that had previously arisen in literature in dissimilar settings. Additionally, given a non-zero sequence satisfying the above recurrence, we evaluate the Hankel transform of the sequence of its reciprocals.

Citations

• Fibonacci numbers and orthogonal polynomials

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