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2. Taylor expansions for the moments of functions of random ...

   en.wikipedia.org/wiki/Taylor_expansions_for_the...

   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.

3. First-order second-moment method - Wikipedia

   en.wikipedia.org/wiki/First-order_second-moment...

   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]

4. Taylor series - Wikipedia

   en.wikipedia.org/wiki/Taylor_series

   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 ...

5. Taylor's theorem - Wikipedia

   en.wikipedia.org/wiki/Taylor's_theorem

   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 .

6. Universal Taylor series - Wikipedia

   en.wikipedia.org/wiki/Universal_Taylor_series

   Thus to -approximate () = using a polynomial with lowest degree 3, we do so for () with < / by truncating its Taylor expansion. Now iterate this construction by plugging in the lowest-degree-3 approximation into the Taylor expansion of g ( x ) {\displaystyle g(x)} , obtaining an approximation of lowest degree 9, 27, 81...

7. Scoring algorithm - Wikipedia

   en.wikipedia.org/wiki/Scoring_algorithm

   Printable version; In other projects ... and consider a Taylor expansion of the score function, ... This page was last edited on 2 November 2024, ...

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9. Isserlis' theorem - Wikipedia

   en.wikipedia.org/wiki/Isserlis'_theorem

   That is, we need only find the coefficient of term in the Taylor expansion of /. If n {\displaystyle n} is odd, this is zero. So let n = 2 m {\displaystyle n=2m} , then we need only find the coefficient of term v 1 ⋯ v n {\displaystyle v_{1}\cdots v_{n}} in the polynomial 1 m !