Shaoshi Chen, Chinese Academy of Sciences, Beijing
"Creative Telescoping for Algebraic Functions"
The problem of finding linear differential equations with polynomial
coefficients for parametric integrals has a long history. It at least dates back to Picard in 1902 who proved the existence of such equations for integrals of algebraic functions involving parameters, nowadays so-called
Picard-Fuchs equations. This has been generalized to higher-dimensional cases and led to Gauss–Manin connections. The key in computer algebra systems for obtaining such linear differential equations is the method of creative telescoping, which was first formulated by Zeilberger in the 1990s as an algorithmic tool for evaluating definite integrals and sums with parameters. The method also enables us to prove a large number of combinatorial identities in an automatic way. In this talk, I will present some recent work on creative telescoping for algebraic functions.
(Joint work with Manuel Kauers, Christoph Koutschan and Michael F. Singer)