A List of Integral Representations for Diagonals of Power Series of Rational Functions
In this article, we present the integral representations of the power series diagonals. Such representations are obtained by lowering the integration multiplicity for the previously known integral representation. The procedure is carried out within the framework of Leray's residue theory. The concept of the amoeba of the complex analytical hypersurface plays an essential role in the construction of new integral representations.