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Error and Complementary Error Functions

Error and Complementary Error FunctionsReadingProblemsOutlineBackgroun d.. 2 Definitions.. 4 Theory.. 6 Gaussian function.. 6 Error function.. 8 Complementary Error function.. 10 Relations and Selected Values of Error Functions .. 12 Numerical Computation of Error Functions .. 19 Rationale Approximations of Error Functions .. 21 Assigned Problems.. 23 References.. 271 BackgroundThe Error function and the Complementary Error function are important special functionswhich appear in the solutions of diffusion problems in heat, mass and momentum transfer,probability theory, the theory of errors and various branches of mathematical physics.

tal functions. The Gaussian probability distribution with mean and standard deviation ˙ is a normalized Gaussian function of the form G(x) = 1 p 2ˇ˙ e (x )2=(2˙2) (1.1) where G(x), as shown in the plot below, gives the probability that a variate with a Gaussian distribution takes on a value in the range [x;x+ dx]. Statisticians commonly ...

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