Asymptotics of Certain Sums Required in Loop Regularisation

Abstract

We consider the three conjectures stated in a 2003 paper of Wu, concerning the asymptotics of particular sums of products of binomials, powers and logarithms. These sums relate to the form of the regularised integrals used in loop regularisation. We show all three are true, extend them to more general powers and produce their full asymptotic series. We also extend a classical result to produce an exact formula for the sum in the last.

Preprint of an article published in Mod. Phys. Lett. A, 16 pages

References in corpus (3)

• Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum
• One-Loop Renormalization of Non-Abelian Gauge Theory and βFunction Based on Loop Regularization Method
• Quantum Structure of Field Theory and Standard Model Based on Infinity-free Loop Regularization/Renormalization

Cited by in corpus (2)

• Gravidynamics, spinodynamics and electrodynamics within the framework of gravitational quantum field theory
• Quadratic Contributions of Softly Broken Supersymmetry in the Light of Loop Regularization