The integrals in Gradshteyn and Ryzhik. Part 10: the digamma function

TL;DR

This paper explores how many integrals listed in Gradshteyn and Ryzhik's table can be expressed using the digamma function, providing explicit evaluations for these integrals.

Contribution

It presents new explicit evaluations of classical integrals in terms of the digamma function, expanding the known connections between integrals and special functions.

Findings

Several integrals are expressed explicitly using the digamma function.

New formulas linking integrals to the digamma function are derived.

The paper enhances the understanding of integral evaluations involving special functions.

Abstract

Many integrals in the classical table by Gradshteyn and Ryzhik can be evaluated in terms of the digamma function (= the logarithmic derivative of the gamma function). Some of them are presented here.