A common formula for certain generalized Hankel transforms

Details A common formula for certain generalized Hankel transforms A common formula for certain generalized Hankel transforms

2009-12-03

arxiv.org/abs/0912.0684v2

Mathematics

Combinatorics

10 pages. Not for publication

Scientific paper

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.

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