Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-07-03
Nucl.Phys.B809:365-405,2009
Physics
High Energy Physics
High Energy Physics - Theory
48 pages in LaTeX
Scientific paper
10.1016/j.nuclphysb.2008.08.022
We prove the following theorems: 1) The Laurent expansions in epsilon of the Gauss hypergeometric functions 2F1(I_1+a*epsilon, I_2+b*epsilon; I_3+p/q + c epsilon; z), 2F1(I_1+p/q+a*epsilon, I_2+p/q+b*epsilon; I_3+ p/q+c*epsilon;z), 2F1(I_1+p/q+a*epsilon, I_2+b*epsilon; I_3+p/q+c*epsilon;z), where I_1,I_2,I_3,p,q are arbitrary integers, a,b,c are arbitrary numbers and epsilon is an infinitesimal parameter, are expressible in terms of multiple polylogarithms of q-roots of unity with coefficients that are ratios of polynomials; 2) The Laurent expansion of the Gauss hypergeometric function 2F1(I_1+p/q+a*epsilon, I_2+b*epsilon; I_3+c*epsilon;z) is expressible in terms of multiple polylogarithms of q-roots of unity times powers of logarithm with coefficients that are ratios of polynomials; 3) The multiple inverse rational sums (see Eq. (2)) and the multiple rational sums (see Eq. (3)) are expressible in terms of multiple polylogarithms; 4) The generalized hypergeometric functions (see Eq. (4)) are expressible in terms of multiple polylogarithms with coefficients that are ratios of polynomials.
Kalmykov Mikhail Yu.
Kniehl Bernd A.
No associations
LandOfFree
Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-115888