ON AN APPLICATION OF THE MULTIPLE LOGARITHMIC RESIDUE TO THE EXPANSION OF IMPLICIT FUNCTIONS IN POWER SERIES
A P Južakov · Mathematics of the USSR-Sbornik · 1975
By means of a multidimensional analog of the theorem of logarithmic residues, representations are found for the implicit functions , , defined by the system of equations where , , , and as also for the function , , where and are holomorphic functions at , in the form of power series and certain function series. In particular, a formula is obtained for the inverse of a holomorphic map in . One degenerate case is considered, where it is still possible to define single-valued branches of the implicit functions.Bibliography: 16 titles.