New results for a two-loop massless propagator-type Feynman diagram

TL;DR

This paper proves the equivalence of two known hypergeometric function representations of a two-loop massless propagator Feynman diagram and introduces new formulas that could aid in calculations.

Contribution

It analytically demonstrates the equality of two existing hypergeometric representations and derives new expressions for the two-loop massless propagator diagram.

Findings

Proved the equivalence of two hypergeometric function representations.

Derived new practical formulas for the Feynman diagram.

Enhanced tools for calculations in quantum field theory.

Abstract

We consider the two-loop massless propagator-type Feynman diagram with an arbitrary (non-integer) index on the central line. We analytically prove the equality of the two well-known results existing in the literature which express this diagram in terms of ${}_3F_2$-hypergeometric functions of argument $-1$ and $1$, respectively. We also derive new representations for this diagram which may be of importance in practical calculations.