Appell F1, F3, Lauricella FD(3), and Lauricella-Saran FS(3) Analytic Continuations and Numerical Evaluation for Feynman Integrals

Multivariable hypergeometric functions are analyzed for analytic continuations and numerical evaluations, particularly focusing on Appell F1, F3, Lauricella FD(3), and Lauricella-Saran FS(3) for applications in Feynman integrals.