Integrals of Frullani type and the method of brackets

Abstract

Abstract:The method of brackets is a collection of heuristic rules, some of which have being made rigorous, that provide a flexible, direct method for the evaluation of definite integrals. The present work uses this method to establish classical formulas due to Frullani which provide values of a specific family of integrals. Some generalizations are established.

A Fourier Integral Formula for Logarithmic Energy

“…This may be seen as a continuous version of (1). It implies in particular that the energy integral is positive definite on the space M 00 (R n ).…”

On the Quenched Free Energy of JT Gravity and Supergravity

“…A line is placed over the Gamma-function here because the symbol Γ is already in use in the paper to label different Bessel and JT supergravity models 9. This is all formalised in the "method of brackets", (reviewed in this Frullani context in ref [84]…”