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We consider the Mellin–Barnes (MB) transform of the triangle ladder-like scalar diagram in d=4 dimensions. It is shown how the multi-fold MB transform of the momentum integral corresponding to an arbitrary number of rungs is reduced to the two-fold MB transform. For this purpose, we use the Belokurov–Usyukina reduction method for four-dimensional scalar integrals in position space. The result is represented...
In our previous paper (Allendes et al., 2013 [10]), we showed that multi-fold Mellin–Barnes (MB) transforms of 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...
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