Multivariable function approximation by using fluctuationlessness approximation applied on a weighted Taylor expansion with remainder term

Based on the Taylor's Theorem for functions of several variables, a newly developed formulation is applied to approximate the remainder term of the multivariate and weighted Taylor polynomial by means of the recently developed Fluctuation Theorem. This new formulation is meant to be used for highly oscillating and/or non-analytic functions of many variables which in fact depresses the use of the Fluctuationlessness approximation.