Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case
Abstract
The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is discussed in the context of evaluating Feynman diagrams. Where this is possible, we compare our results with those obtained using standard techniques. It is shown that the criterion of reducibility of multiloop Feynman integrals can be reformulated in terms of the criterion of reducibility of hypergeometric functions. The relation between the numbers of master integrals obtained by differential reduction and integration by parts is discussed.
Cite
@article{arxiv.0904.0214,
title = {Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case},
author = {Vladimir V. Bytev and Mikhail Yu. Kalmykov and Bernd A. Kniehl},
journal= {arXiv preprint arXiv:0904.0214},
year = {2010}
}
Comments
46 pages in LaTeX; 2 eps figures; v3. Section 3 improved; Section 4 changed; new References added; version published in Nucl. Phys. B;