# On some new moments of Gamma type

## TL;DR

This paper explores positive random variables with moments of Gamma type, providing conditions for their existence and using Bessel functions to construct non-trivial examples with signed spectral measures.

## Contribution

It introduces new conditions for the existence of moments of Gamma type and demonstrates how Bessel functions can be used to construct such moments with signed spectral measures.

## Key findings

- Conditions for existence of moments of Gamma type
- Construction of non-trivial moments using Bessel functions
- Identification of signed spectral measures in these constructions

## Abstract

We investigate certain positive random variables having moments of Gamma type. Some necessary and some sufficient conditions are given for their existence. In particular, we observe that the Weber-Schafheitlin formula for the Bessel function makes it possible to construct non-trivial moments of Gamma type having a signed spectral measure.