The Lagrangian remainder of Taylor's series, distinguishes O(f(x)) time complexities to polynomials or not

01/30/2020

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by   Nikolaos P. Bakas, et al.

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The purpose of this letter is to investigate the time complexity consequences of the truncated Taylor series, known as Taylor Polynomials <cit.>. In particular, it is demonstrated that the examination of the P=NP equality, is associated with the determination of whether the n^th derivative of a particular solution is bounded or not. Accordingly, in some cases, this is not true, and hence in general.