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A Gaussian sum is a sum of the form S(p,q)=sum_(r=0)^(q-1)e^(-piir^2p/q), (1) where p and q are relatively prime integers. The symbol phi is sometimes used instead of S. ...

Finch (2010) gives an overview of known results for random Gaussian triangles. Let the vertices of a triangle in n dimensions be normal (normal) variates. The probability ...

The inverse Gaussian distribution, also known as the Wald distribution, is the distribution over [0,infty) with probability density function and distribution function given ...

The Fourier transform of a Gaussian function f(x)=e^(-ax^2) is given by F_x[e^(-ax^2)](k) = int_(-infty)^inftye^(-ax^2)e^(-2piikx)dx (1) = ...

The Gaussian joint variable theorem, also called the multivariate theorem, states that given an even number of variates from a normal distribution with means all 0, (1) etc. ...

If x_1<x_2<...<x_n denote the zeros of p_n(x), there exist real numbers lambda_1,lambda_2,...,lambda_n such that ...

The definite integral int_a^bx^ndx={(b^(n+1)-a^(n+1))/(n+1) for n!=1; ln(b/a) for n=-1, (1) where a, b, and x are real numbers and lnx is the natural logarithm.

A coordinate system which has a metric satisfying g_(ii)=-1 and partialg_(ij)/partialx_j=0.

A quadrature (numerical integration) algorithm which has a number of desirable properties.

R(p,tau) = int_(-infty)^inftyint_(-infty)^infty[1/(sigmasqrt(2pi))e^(-(x^2+y^2)/(2sigma^2))]delta[y-(tau+px)]dydx (1) = ...