A common formula for certain generalized Hankel transforms

Abstract

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

10 pages. Not for publication

References in corpus (1)

• Fibonacci numbers and orthogonal polynomials