Some explicit formulas for a sequence of secondary measures

TL;DR

This paper derives explicit formulas for the density functions of a sequence of secondary measures, providing insights into their structure and applications, including interpretations of Fourier coefficients as multiple integrals.

Contribution

It introduces explicit formulas for the densities of secondary measures and offers new interpretations of Fourier coefficients as multiple integrals.

Findings

Explicit formulas for densities of secondary measures

Applications to orthogonal polynomials and Fourier analysis

Interpretation of Fourier coefficients as multiple integrals

Abstract

We study here a sequence of secondary measures, so called because the set of secondary polynomials on a given term become orthogonal for the next measure. The main result is a formula making explicit the density of any term of the sequence, under some hypotheses. We give some applications and also derive an interpretation of the Fourier coefficients as multiple integrals.