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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), whereI_1,I_2,I_3,p,q are arbitrary integers, a,b,c are arbitrary numbers and epsilonis an infinitesimal parameter, are expressible in terms of multiplepolylogarithms of q-roots of unity with coefficients that are ratios ofpolynomials; 2) The Laurent expansion of the Gauss hypergeometric function2F1(I_1+p/q+a*epsilon, I_2+b*epsilon; I_3+c*epsilon;z) is expressible in termsof multiple polylogarithms of q-roots of unity times powers of logarithm withcoefficients that are ratios of polynomials; 3) The multiple inverse rationalsums (see Eq. (2)) and the multiple rational sums (see Eq. (3)) are expressiblein terms of multiple polylogarithms; 4) The generalized hypergeometricfunctions (see Eq. (4)) are expressible in terms of multiple polylogarithmswith coefficients that are ratios of polynomials.

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