Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters

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dc.creatorKalmykov, Mikhail Yu.
dc.creatorKniehl, Bernd A.
dc.date2008-07-03
dc.date.accessioned2026-07-07T12:34:03Z
dc.date.available2026-07-07T12:34:03Z
dc.descriptionWe 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.
dc.description48 pages in LaTeX
dc.identifierhttps://arxiv.org/abs/0807.0567
dc.identifierhttp://arxiv.org/abs/0807.0567
dc.identifierNucl.Phys.B809:365-405,2009
dc.identifierdoi:10.1016/j.nuclphysb.2008.08.022
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217286
dc.subjectHigh Energy Physics - Theory
dc.subjectHigh Energy Physics - Phenomenology
dc.subjectMathematical Physics
dc.subjectClassical Analysis and ODEs
dc.titleTowards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters
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