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Planck's's radiation function is the function f(x)=(15)/(pi^4)1/(x^5(e^(1/x)-1)), (1) which is normalized so that int_0^inftyf(x)dx=1. (2) However, the function is sometimes ...

There are at least two integrals called the Poisson integral. The first is also known as Bessel's second integral, ...

The integral kernel in the Poisson integral, given by K(psi)=1/(2pi)(1-|z_0|^2)/(|z_0-e^(ipsi)|^2) (1) for the open unit disk D(0,1). Writing z_0=re^(itheta) and taking ...

The signature of a non-degenerate quadratic form Q=y_1^2+y_2^2+...+y_p^2-y_(p+1)^2-y_(p+2)^2-...-y_r^2 of rank r is most often defined to be the ordered pair (p,q)=(p,r-p) of ...

A Gaussian quadrature-like formula for numerical estimation of integrals. It requires m+1 points and fits all polynomials to degree 2m, so it effectively fits exactly all ...

R(p,tau)=int_(-infty)^inftyint_(-infty)^inftyf(x,y)delta[y-(tau+px)]dydx, (1) where f(x,y)={1 for x,y in [-a,a]; 0 otherwise (2) and ...

On a three-dimensional lattice, a random walk has less than unity probability of reaching any point (including the starting point) as the number of steps approaches infinity. ...

A square n×n matrix A=a_(ij) is called reducible if the indices 1, 2, ..., n can be divided into two disjoint nonempty sets i_1, i_2, ..., i_mu and j_1, j_2, ..., j_nu (with ...

The regularized gamma functions are defined by P(a,z) = (gamma(a,z))/(Gamma(a)) (1) Q(a,z) = (Gamma(a,z))/(Gamma(a)), (2) where gamma(a,z) and Gamma(a,z) are incomplete gamma ...

For a set of n numbers or values of a discrete distribution x_i, ..., x_n, the root-mean-square (abbreviated "RMS" and sometimes called the quadratic mean), is the square ...