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Moment sequences of Beta distribution

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arxiv 2112.13420 v3 pith:C7QGYAUB submitted 2021-12-26 math.PR

Pawe{l} J. Szab{l}owski This is my paper · ORCID
classification math.PR
keywords sequencesbetadistributionsmomentsomecatalandistributionidentified
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abstract

We recall some basic properties of the Beta distribution and some of its modifications. We identified around $20$ of the moment sequences of Beta distributions as important integer sequences in the OEIS base of integer sequences. Among those identified are Catalan, Riordan, Motzkin, or 'super ballot numbers'. By applying a method of expansion of the ratio of densities of involved distributions we are able to obtain some known and many unknown relationships between e.g. Catalan numbers and other moment sequences of the Beta distributions.

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Cited by 1 Pith paper

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  1. Spectral Obstructions to Contracting Transport Maps on Curved Spaces

    math.DG 2026-05 unverdicted novelty 7.0 of 10

    Explicit metrics on S^d and weighted R^d for d≥4 violate Milman's spectral comparison conjectures, ruling out 1-Lipschitz transport maps; the abstract's extra dimension-2 and hemisphere results are not in the text.

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