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We investigate the structure of the constraints on three-point correlationfunctions emerging when conformal invariance is imposed in momentum space andin arbitrary space-time dimensions, presenting a derivation of their solutionsfor arbitrary scalar operators. We show that the differential equationsgenerated by the requirement of symmetry under special conformaltransformations coincide with those satisfied by generalized hypergeometricfunctions (Appell's functions). Combined with the position space expression ofthis correlator, whose Fourier transform is given by a family of generalizedFeynman (master) integrals, the method allows to derive the expression of suchintegrals in a completely independent way, bypassing the use of Mellin-Barnestechniques, which have been used in the past. The application of the specialconformal constraints generates a new recursion relation for this family ofintegrals.

Solving the Conformal Constraints for Scalar Operators in Momentum Space and the Evaluation of Feynman's Master Integrals