Schneider C., Blümlein J. (Eds.) Computer Algebra in Quantum Field Theory. Integration, Summation and Special Functions

Springer Wien, 2013. — 411 p. — (Texts & Monographs in Symbolic Computation). — ISBN: 978-3-7091-1616-6, 978-3-7091-1615-9.The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.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 N_f Methods
The Holonomic Toolkit
Orthogonal Polynomials
Creative Telescoping for Holonomic Functions
Renormalization and Mellin Transforms
Relativistic Coulomb Integrals and Zeilberger’s Holonomic Systems Approach. I
Hypergeometric Functions in Mathematica
Solving Linear Recurrence Equations with Polynomial Coefficients
Generalization of Risch’s Algorithm to Special Functions
Multiple Hypergeometric Series: Appell Series and Beyond
Simplifying Multiple Sums in Difference Fields
Potential of FORM 4.0
Feynman Graphs