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 (18)

• 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
• Series representations of the Riemann and Hurwitz zeta functions and series and integral representations of the first Stieltjes constant
• Various applications of the (exponential) complete Bell polynomials
• Certain logarithmic integrals, including solution of Monthly problem #tbd, zeta values, and expressions for the Stieltjes constants
• Sums of alternating products of Riemann zeta values and solution of a Monthly problem
• On harmonic sums and alternating Euler sums
• A Faster Product for Pi and a New Integral for ln(Pi/2)
• Logarithmic Integrals, Polylogarithmic Integrals and Euler sums
• Some trigonometric integrals involving the log gamma and the digamma function
• Double Integrals for Euler's Constant and ln(4/Pi) and an Analog of Hadjicostas's Formula
• Construction of the Digamma Function by Derivative Definition
• Some applications of the Beta function

Cited by in corpus (5)

• A special constant and series with zeta values and harmonic numbers
• Generalizations of the Euler-Mascheroni constant associated with the hyperharmonic numbers
• Some relations involving the higher derivatives of the Riemann zeta function
• Closed-form expressions for Farhi's constant and related integrals and its generalization
• On some new formulae involving the Stieltjes constants