On an integral involving the digamma function

Abstract

We consider several possible approaches to evaluating an integral involving the digamma function and a related logarithmic series.

References in corpus (15)

• The generalized-Euler-constant function $\gamma (z)$ and a generalization of Somos's quadratic recurrence constant
• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume I
• Theta and Riemann xi function representations from harmonic oscillator eigensolutions
• The integrals in Gradshteyn and Rhyzik. Part 1: A family of logarithmic integrals
• Some applications of the Stieltjes constants
• The integrals in Gradshteyn and Ryzhik. Part 11: The incomplete beta function
• The difference between two Stieltjes constants
• Various applications of the (exponential) complete Bell polynomials
• Series representations of the Riemann and Hurwitz zeta functions and series and integral representations of the first Stieltjes constant
• Sums of alternating products of Riemann zeta values and solution of a Monthly problem
• On harmonic sums and alternating Euler sums
• Logarithmic Integrals, Polylogarithmic Integrals and Euler sums
• Some trigonometric integrals involving the log gamma and the digamma function
• Construction of the Digamma Function by Derivative Definition
• Some applications of the Beta function