2007/08/31 by M. Yu. Kalmykov, Mikhail Y Kalmykov, B. F. L. Ward +3
Computer Science · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Basic hypergeometric series #Bilateral hypergeometric series #Confluent hypergeometric function #Frobenius solution to the hypergeometric equation #Generalized hypergeometric function #Hypergeometric distribution #Hypergeometric function #Hypergeometric function of a matrix argument #Hypergeometric identity #Mathematical functions and polynomials #Polynomial and algebraic computation #hep-ph #hep-th #math-ph #math.CA #math.MP
paper · pdf · doi:10.1088/1126-6708/2007/11/009
published as JHEP 0711:009,2007 · 12 pages, Latex + amsmath, JHEP3 class packages. This revision adds references 1 and 19. The FORM code is available via the WWW at http://theor.jinr.ru/~kalmykov/hypergeom/hyper.html
openalex publication_date 2007/11/06 · arxiv created 2007/11/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We continue our study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we apply the approach of obtaining iteratated solutions to the differential equations associated with hypergeometric functions to prove the following result (Theorem 1): The epsilon-expansion of a generalized hypergeometric function with integer values of parameters is expressible in terms of generalized polylogarithms with coefficients that are ratios of polynomials. The method used in this proof provides an efficient algorithm for calculatiing of the higher-order coefficients of Laurent expansion.