# Asymptotic Series Error Function

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Asymptotic expansion of the complementary error function. For the complementary error function erfc(x), the asymptotic series has a minimum error.

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The (complete) gamma function Gamma(n) is defined to be an extension of the factorial to complex and real number arguments. It is related to the factorial by Gamma(n.

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Function to compute augmentation MTP adjusted p-values – A function for control. "Resampling-based Multiple Testing: Asymptotic Control of Type I Error and Applications to Gene Expression Data" (June 24, 2003). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper.

In mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the.

Mar 13, 2014. see §§2.11(ii)–2.11(iv) and use (7.11.3). (Note that some of these re- expansions themselves involve the complementary error function.).

Erf — from Wolfram MathWorld – is the "error function" encountered in integrating the normal distribution (which is a normalized form. and continuing the procedure gives the asymptotic series.

erf(z) is the "error function" encountered in integrating the normal distribution (which is a normalized form of the Gaussian function). It is an entire function.

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The asymptotic series for this function can be generated via a series of. The relative error in a typical asymptotic series plotted as a function of the number of.

The benefits of using an analytical approximation for error function in. By using the Taylor expansion inversely, a variant of Equation (5) is. unwieldy and unhelpful description based on asymptotic expansions to both ends when it is, in fact,

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In mathematics, the error function is a special function (non-elementary) of sigmoid shape that occurs in probability,

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Physics 116A. Asymptotic expansion of the complementary error function. Peter Young. (Dated: January 28, 2014). For the complementary error function erfc(x),

The name "error function" The error function is used in measurement theory (using probability and statistics), and its use in other branches of mathematics is.

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2.2.1 Asymptotic power series. is very slow. the Taylor series of the error function at x = 0. Instead, we can use the following divergent asymptotic expansion,

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Taylor series. The error function is an entire function;. Asymptotic expansion. A useful asymptotic expansion of the complementary error function.

An asymptotic expansion describes the asymptotic behavior of a function in terms. series of the error function at x = 0 provides a poor approximation of the.