Refined Holonomic Summation Algorithms in Particle Physics

Understand

An improved multi-summation approach is introduced and discussed that enables one to simultaneously handle indefinite nested sums and products in the setting of difference rings and holonomic sequences.

• Relevant mathematics is reviewed and the underlying advanced difference ring machinery is elaborated upon.
• The flexibility of this new toolbox contributed substantially to evaluating complicated multi-sums coming from particle physics.
• Illustrative examples of the functionality of the new software package RhoSum are given.