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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 .
Since a second-order expansion for [()] has already been derived above, it only remains to find [() ()]. Treating f ( X ) f ( Y ) {\displaystyle f(X)f(Y)} as a two-variable function, the second-order Taylor expansion is as follows:
That is, the Taylor series diverges at x if the distance between x and b is larger than the radius of convergence. The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point. Uses of the Taylor series for analytic functions ...
Download as PDF; Printable version; ... be random variables, ... and consider a Taylor expansion of the score function, ...
Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices.
Download as PDF; Printable version; ... or the more general Sonine formula [2] ... the Taylor expansion (addition formula) ...
Taylor expansion. Add languages. Add links. Article; Talk; English. ... Download as PDF; Printable version; In other projects Appearance. move to sidebar hide. From ...
The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems. [1]