Representing Spenceʹs integral by elementary functions Original Research Article

An interesting connection exists between Spenceʹs integral, used in Feynman diagrams in particle physics, and the variance of the reciprocal of a geometric random variable, used in probability theory. This linkage leads to approximate representations for Spenceʹs integral over the unit interval which works well in practice. The result shows how the interplay between probability and physics can bear pragmatic fruit.