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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. A simulation-based alternative to this approximation is the application of Monte Carlo simulations.
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 ...
Print/export Download as PDF; ... be random variables, independent ... and consider a Taylor expansion of the score function, ...
Now its Taylor series centered at z 0 converges on any disc B(z 0, r) with r < |z − z 0 |, where the same Taylor series converges at z ∈ C. Therefore, Taylor series of f centered at 0 converges on B(0, 1) and it does not converge for any z ∈ C with |z| > 1 due to the poles at i and −i.
The usage of the term "Grassmann variables" is historic; they are not variables, per se; they are better understood as the basis elements of a unital algebra. The terminology comes from the fact that a primary use is to define integrals, and that the variable of integration is Grassmann-valued, and thus, by abuse of language, is called a ...
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.
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]
Download as PDF; Printable version; In other projects ... has Taylor expansion in the chart: ... Note that this transformation formula is for the mean curvature ...
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