Maclaurin series by integration
Summary: In this note we obtain Maclaurin series of the functions arctan \(x\), \(\ln(1+x)\) and \(\arctan x + \ln \sqrt{1+x^2}\) for \(x \in [0, 1]\) by using integration by parts, and we give explicit integral representations for the error terms in their truncated Maclaurin series.
scientific article; zbMATH DE number 7364019