Analytic results for some types of Feynman integrals at any loop order

Abstract In this paper, we investigate three types of Feynman integrals up to any loop, including the massless banana integral, the one-mass banana integral, and the massless three-point multi-edge integral. Although these integrals are simple in topology, they are involved in many interesting processes, like heavy quarks production and decay, as well as massless quark gluon form factors. By using one-loop integration formulas recursively, we obtain the analytic results at any loop order. It turns out that the results are quite simple and compact. The calculation method used in this work is straightforward, and may be generalized to more general cases.