This book deals with integral representations of holomorphic functions of several complex variables, the multidimensional logarithmic residue, and the theory of multidimensional residues. Applications are given to implicit function theory, systems of nonlinear equations, computation of the multiplicity of a zero of a mapping, and computation of combinatorial sums in closed form. Certain applications in multidimensional complex analysis are considered. The monograph is intended for specialists in theoretical and applied mathematics and theoretical physics, and for postgraduate and graduate students interested in multidimensional complex analysis or its applications.
I. Integral representations and the logarithmic residue II. Integral representations of special form for holomorphic functions III. The theory of residues IV. Applications to implicit functions, systems of nonlinear equations, computation of the multiplicity of a zero, and combinatorics V. Some applications in multidimensional complex analysis.