Nested Taylor Decomposition of Univariate Functions under Fluctuationlessness Approximation

Abstract

Taylor decomposition of an analytic function and the use of the remainder part of this decomposition expressed in integral form on which Fluctuationlessness theorem is applied was already known in the litterature, but application of Fluctuationlessness approximation twice on the remainder part adds up an amelioration to the approximation. Organisation of the decomposition in such a way that this is made possible is explained in detail in this work.