Hypergeometric Functions and Feynman Diagrams

The relationship between Feynman diagrams and hypergeometric functions is discussed. Special attention is devoted to existing techniques for the construction of the epsilon-expansion. As an example, we present a detailed discussion of the construction of the epsilon-expansion of the Appell function F3 around rational values of parameters via an iterative solution of differential equations. Another interesting example is the Puiseux-type solution involving a differential operators generated by a hypergeometric function of three variables. The holonomic properties of the $F_N$ hypergeometric functions is briefly discussed