A common formula for certain generalized Hankel transforms

Mario Garcia-Armas

A common formula for certain generalized Hankel transforms

Combinatorics 2012-03-27 v2

Authors: Mario Garcia-Armas

Abstract

We study the generalized Hankel transform of the family of sequences satisfying the recurrence relation $a_{n+1} = \bigl(\alpha + \frac{\beta}{n+\gamma}\bigr) a_n$ . 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.

Keywords

integer sequences and recurrences generalization theorems collatz conjecture

Cite

@article{arxiv.0912.0684,
  title  = {A common formula for certain generalized Hankel transforms},
  author = {Mario Garcia-Armas},
  journal= {arXiv preprint arXiv:0912.0684},
  year   = {2012}
}

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10 pages. Not for publication

A common formula for certain generalized Hankel transforms

Abstract

Keywords

Cite

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