Examples of automatic asymptotic expansions

Automatic application of successive asymptotic expansions of Feynman diagrams

We discuss the program EXP used to automate the successive application of asymptotic expansions to Feynman diagrams. We focus on the generation of the relevant subgraphs and the determination of the topologies for the remaining integrals. Both tasks can be solved by using backtracking-type recursive algorithms. In addition, an application of EXP is presented, where the integrals were calculated...

Asymptotic Expansions

Asymptotic expansions of functions are useful in statistics in three main ways. Firstly, conventional asymptotic expansions of special functions are useful for approximate computation of integrals arising in statistical calculations. An example given below is the use of Stirling's approximation to the gamma function. Second, asymptotic expansions of density or distribution functions of estimato...

Asymptotic Expansions Methodsand Applications

Feynman diagrams are the most important theoretical tool for particle physicists. They are an efficient link between theory and experiment. However, their translation into actual numerical predictions is often very tedious if not impossible. Huge efforts have been devoted to their evaluation, and several powerful methods have been developed to systemize their treatment. The more complex a Feynm...

Asymptotic Expansions for Integrals

Asymptotic Expansions of exp - log

We give an algorithm to compute asymptotic expansions of exp-log functions. This algorithm automatically computes the necessary asymptotic scale and does not suuer from problems of indeenite cancellation. In particular, an asymptotic equivalent can always be computed for a given exp-log function. D eveloppements asymptotiques de fonctions exp-log R esum e Nous pr esentons un algorithme pour le ...