The iterated integrals of ln(1 + x^2)

TL;DR

This paper explores the properties of iterated integrals of logarithmic functions of polynomials, focusing on ln(1 + x^2), revealing connections to polynomial zeros and arithmetic properties of coefficients.

Contribution

It provides a novel analysis of iterated integrals of ln P(x), expressing them via polynomial zeros and examining specific cases like ln(1 + x^2).

Findings

Expressed iterated integrals in terms of polynomial zeros

Described arithmetic properties of coefficients for ln(1 + x^2)

Made similar observations for ln(1 + x^3)

Abstract

For a polynomial P, we consider the sequence of iterated integrals of ln P(x). This sequence is expressed in terms of the zeros of P(x). In the special case of ln(1 + x^2), arithmetic properties of certain coefficients arising are described. Similar observations are made for ln(1 + x^3).