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

Tewodros Amdeberhan, Christoph Koutschan, Victor H. Moll, Eric S. Rowland

Published 2010-12-15, updated 2011-04-05Version 2

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).