Extended fluctuationlessness theorem and its application to numerical integration via Taylor series

Abstract

According to the Fluctuationlessness Theorem, the matrix representation of a function is approximately equal to the image of the matrix representation of its independent variable under the same function, in the Hilbert space of square integrable functions. In this work Extended Fluctuationlessness theorem applied to the finite integral of the Taylor expansion is taken into consideration to form a new quadrature.