This book focuses on advanced computer algebra methods and special functions that have applications in quantum field theory. It presents new methods for (infinite) multiple sums, multiple integrals, difference and differential equations.

Combines techniques methods from special functions and computer algebra applied to quantum field theory Contains survey articles written by mathematicians and physicists Describes algorithms and techniques developed by interdisciplinary teams of mathematicians, theoretical particle physicists and computer scientists Includes supplementary material: sn.pub/extras

Inhalt
Harmonic sums, polylogarithms, special numbers, and their generalizations.- Multiple Zeta values and modular forms in quantum field theory.- Computer-assisted proofs of some identities for Bessel functions of fractional order.- Conformal methods for massless Feynman integrals and large Nf methods.- The holonomic toolkit.- Orthogonal polynomials.- Creative telescoping for holonomic functions.- Renormalization and Mellin transforms.- Relativistic Coulomb integrals and Zeilberger's holonomic systems approach.- Hypergeometric functions in Mathematica.- Solving linear recurrence equations with polynomial coefficients.- Generalization of Risch's algorithms to special functions.- Multiple hypergeometric series.- Appell series and beyond.- Simplifying multiple sums in difference fields.- Potential of FORM 4.0.- Feynman graphs.