A common formula for certain generalized Hankel transforms
Abstract
We study the generalized Hankel transform of the family of sequences satisfying the recurrence relation an+1 = (α + βn+γ) an. 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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