# One-loop three-point Feynman integrals with Appell $F_1$ hypergeometric functions

## TL;DR

This paper derives new analytic formulas for one-loop three-point Feynman integrals in general dimensions, expressing them with Appell $F_1$ hypergeometric functions for broad configurations of masses and momenta.

## Contribution

The paper introduces a novel analytic expression for these integrals using Appell $F_1$ functions applicable to general configurations, extending previous special-case results.

## Key findings

- Analytic formulas expressed in hypergeometric functions for general configurations.
- Cross-checked results with existing literature for special cases.
- Provides a unified approach for different mass and momentum configurations.

## Abstract

New analytic formulas for one-loop three-point Feynman integrals in general space-time dimension ($d$) are presented in this paper. The calculations are performed at general configurations for internal masses and external momenta. The analytic results are expressed in terms of hypergeometric series $_2F_1$, $_3F_2$ for special cases and Appell $F_1$ for general cases. Furthermore, we cross-check our analytic results with other references which have carried out the integrals in several special cases.