Differential Reduction Algorithms for the All-Order Epsilon Expansion of Hypergeometric Functions
Scott Alan Yost, M.Yu. Kalmykov, B. F. L. Ward · arXiv (Cornell University) · 2008
Hypergeometric functions provide a useful representation of Feynman diagrams occuring in precision phenomenology. In dimension regularization, the epsilon-expansion of these functions about d=4 is required. We discuss the current status of differential reduction algorithms. As an illustration, we consider the construction of the all-order epsilon-expansion of the Appell hypergeometric function about integer values of the parameters and present an explicit evaluations of the first few terms.