Bernd Kniehl, Igor Kondrashuk, Eduardo A. Notte-Cuello, Ivan Parra Ferrada, Marko Rojas-Medar
In our previous paper (Nucl.Phys.B 870 (2013) 243) we showed that multi-fold Mellin-Barnes (MB) transforms of the Usyukina-Davydychev (UD) functions may be reduced to two-fold MB transforms. The MB transforms were written there as polynomials of logarithms of ratios of squares of the external momenta with certain coefficients. We also showed that these coefficients have a combinatoric origin. In this paper we present an explicit formula for these coefficients. The procedure of recovering the coefficients is based on taking the double uni-form limit in certain series of smooth functions of two variables which is constructed according to a pre-determined iterative way. The result is obtained by using basic methods of mathematical analysis. We observe that the finiteness of the limit of this iterative chain of smooth functions should reflect itself in other mathematical constructions, too, since it is not related in any way to the explicit form of the MB transforms.
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http://arxiv.org/abs/1304.3004
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