Error and Complementary Error Functions
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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www.mhtlab.uwaterloo.caThe first reported use of the gamma symbol for this function was by Legendre in 1839.2 The first Eulerian integral was introduced by Euler and is typically referred to by its more common name, the Beta function. The use of the Beta symbol for this function was first used in 1839 by Jacques P.M. Binet (1786 - 1856).
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www.mhtlab.uwaterloo.caa unit mass situated at the point A is given by φ = C R where C is some constant. It can be shown that this function is a solution of Laplace’s equation.!In some circumstances, it is desirable to expand φ in powers of r or r−1 where r = x 2+y +z is the distance from the origin O to the point P. OA OB AP x y z A(x,y,z) B(x,y,z) a R r O
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www.mhtlab.uwaterloo.catheory of numbers, algebra, geometry, linear and non-linear ordinary and partial differential equations, dynamics, mechanics, electrostatics, conduction and field theory. An elliptic integral is any integral of the general form f(x)= A(x)+B(x) C(x)+D(x)! S(x) dx where A(x),B(x),C(x) and D(x) are polynomials in x and S(x) is a polynomial of ...
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