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  2. Error function - Wikipedia

    en.wikipedia.org/wiki/Error_function

    Download as PDF; Printable version; ... Series definition; Taylor series ... there is a systematic methodology to solve the numerical coefficients ...

  3. Taylor's theorem - Wikipedia

    en.wikipedia.org/wiki/Taylor's_theorem

    The Taylor series of f converges uniformly to the zero function T f (x) = 0, which is analytic with all coefficients equal to zero. The function f is unequal to this Taylor series, and hence non-analytic. For any order k ∈ N and radius r > 0 there exists M k,r > 0 satisfying the remainder bound above.

  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. Normal distribution - Wikipedia

    en.wikipedia.org/wiki/Normal_distribution

    Download as PDF; Printable version; ... Newton's method is ideal to solve this problem because the first derivative of ... from a Taylor series solution using ...

  6. Nonelementary integral - Wikipedia

    en.wikipedia.org/wiki/Nonelementary_Integral

    Nonelementary antiderivatives can often be evaluated using Taylor series. Even if a function has no elementary antiderivative, its Taylor series can always be integrated term-by-term like a polynomial, giving the antiderivative function as a Taylor series with the same radius of convergence. However, even if the integrand has a convergent ...

  7. Experimental uncertainty analysis - Wikipedia

    en.wikipedia.org/wiki/Experimental_uncertainty...

    Even if the PDF can be found, finding the moments (above) can be difficult. 4. The solution is to expand the function z in a second-order Taylor series; the expansion is done around the mean values of the several variables x. (Usually the expansion is done to first order; the second-order terms are needed to find the bias in the mean.

  8. Delta method - Wikipedia

    en.wikipedia.org/wiki/Delta_method

    The intuition of the delta method is that any such g function, in a "small enough" range of the function, can be approximated via a first order Taylor series (which is basically a linear function). If the random variable is roughly normal then a linear transformation of it is also normal. Small range can be achieved when approximating the ...

  9. Analytic function - Wikipedia

    en.wikipedia.org/wiki/Analytic_function

    Furthermore, every polynomial is its own Maclaurin series. The exponential function is analytic. Any Taylor series for this function converges not only for x close enough to x 0 (as in the definition) but for all values of x (real or complex). The trigonometric functions, logarithm, and the power functions are analytic on any open set of their ...