Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-12-21
JHEP 0702:040,2007
Physics
High Energy Physics
High Energy Physics - Theory
18 pages, JHEP3.cls The code (FORM) is available via the www http://theor.jinr.ru/~kalmykov/hypergeom/hyper.html v2: Appendix
Scientific paper
10.1088/1126-6708/2007/02/040
It is proved that the Laurent expansion of the following Gauss hypergeometric functions, 2F1(I1+a*epsilon, I2+b*ep; I3+c*epsilon;z), 2F1(I1+a*epsilon, I2+b*epsilon;I3+1/2+c*epsilon;z), 2F1(I1+1/2+a*epsilon, I2+b*epsilon; I3+c*epsilon;z), 2F1(I1+1/2+a*epsilon, I2+b*epsilon; I3+1/2+c*epsilon;z), 2F1(I1+1/2+a*epsilon,I2+1/2+b*epsilon; I3+1/2+c*epsilon;z), where I1,I2,I3 are an arbitrary integer nonnegative numbers, a,b,c are an arbitrary numbers and epsilon is an arbitrary small parameters, are expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with polynomial coefficients. An efficient algorithm for the calculation of the higher-order coefficients of Laurent expansion is constructed. Some particular cases of Gauss hypergeometric functions are also discussed.
Kalmykov Mikhail Yu.
Ward B. F. L.
Yost Sarah
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