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. Itis interesting to note that there is a direct connection between the Error function and theGaussian function and the normalized Gaussian function that we know as the bell curve .The Gaussian function is given asG(x) =Ae x2/(2 2)where is the standard deviation andAis a Gaussian function can be normalized so that the accumulated area under the curve isunity, the integral from to+ equals1.

The Gaussian function or the Gaussian probability distribution is one of the most fundamen-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 ...

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