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In probability theory, it is possible to approximate the moments of a function f of a random variable X using Taylor expansions, provided that f is sufficiently differentiable and that the moments of X are finite.
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point.
Taylor's theorem is named after the mathematician Brook Taylor, who stated a version of it in 1715, [2] although an earlier version of the result was already mentioned in 1671 by James Gregory. [3] Taylor's theorem is taught in introductory-level calculus courses and is one of the central elementary tools in mathematical analysis.
Download as PDF; Printable version; ... then perform Taylor expansion. ... The same factor of σ 2 / 2 appears in the d 1 and d 2 auxiliary variables of the ...
For the second-order approximations of the third central moment as well as for the derivation of all higher-order approximations see Appendix D of Ref. [3] Taking into account the quadratic terms of the Taylor series and the third moments of the input variables is referred to as second-order third-moment method. [4]
Taylor expansion. Add languages. Add links. Article; Talk; ... Download as PDF; Printable version; ... This page was last edited on 2 June 2010, ...
Download as PDF; Printable version; ... variables one has ... for a smooth enough function, we have the similar Taylor expansion ...
In principle, a multipole expansion provides an exact description of the potential, and generally converges under two conditions: (1) if the sources (e.g. charges) are localized close to the origin and the point at which the potential is observed is far from the origin; or (2) the reverse, i.e., if the sources are located far from the origin ...