The Laplace transform of the digamma function: an integral due to Glasser, Manna and Oloa

Abstract

We provide an analytic expression for the Laplace transform of the digamma fuction. This complements work of L. Glasser, D. Manna and O. Oloa on this question. The Laplace transform is continuous in the Laplace-variable a. The derivative admits a jump at a= ln 2.

10 pages, 1 figure

References in corpus (6)

• The integrals in Gradshteyn and Rhyzik. Part 1: A family of logarithmic integrals
• The integrals in Gradshteyn and Ryzhik. Part 4: The Gamma function
• The integrals in Gradshteyn and Rhyzik. Part 2: Elementary logarithmic integrals
• The integrals in Gradshteyn and Ryzhik. Part 5: Some trigonometric integrals
• The integrals in Gradshteyn and Ryzhik. Part 3: Combinations of Logarithms and Exponentials
• The integrals in Gradshteyn and Ryzhik. Part9: Combinations of logarithms, rational and trigonometric functions