Analytic combinatorics and QFT

In this chapter we present how several analytic techniques, often used in combinatorics, appear naturally in various QFT issues. In the first section we show how one can use the Mellin transform technique to re-express Feynman integrals in a useful way for the mathematical physicist. Finally, we briefly present how the saddle point approximation technique can be also used in QFT. The first phrase of Philippe Flajolet and Robert Sedgewick's encyclopaedic book on analytic combinatorics gives the reader a first glimpse of what analytic combinatorics deals. In the following chapter, we present how several analytic techniques, often used in combinatorics,appear naturally in various QFT issues.