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Just as the ratio of the arc length of a semicircle to its radius is always pi, the ratio P of the arc length of the parabolic segment formed by the latus rectum of any ...

The bivariate normal distribution is the statistical distribution with probability density function P(x_1,x_2)=1/(2pisigma_1sigma_2sqrt(1-rho^2))exp[-z/(2(1-rho^2))], (1) ...

The integral transform obtained by defining omega=-tan(1/2delta), (1) and writing H(omega)=R(omega)+iX(omega), (2) where R(omega) and X(omega) are a Hilbert transform pair as ...

Let {a_n} be a series of positive terms with a_(n+1)<=a_n. Then sum_(n=1)^(infty)a_n converges iff sum_(k=0)^infty2^ka_(2^k) converges.

A test to determine if a given series converges or diverges.

Define the correlation integral as C(epsilon)=lim_(N->infty)1/(N^2)sum_(i,j=1; i!=j)^inftyH(epsilon-|x_i-x_j|), (1) where H is the Heaviside step function. When the below ...

A general space based on the line element ds=F(x^1,...,x^n;dx^1,...,dx^n), with F(x,y)>0 for y!=0 a function on the tangent bundle T(M), and homogeneous of degree 1 in y. ...

The Franel numbers are the numbers Fr_n=sum_(k=0)^n(n; k)^3, (1) where (n; k) is a binomial coefficient. The first few values for n=0, 1, ... are 1, 2, 10, 56, 346, ... (OEIS ...

A link invariant defined for a two-component oriented link as the sum of +1 crossings and -1 crossing over all crossings between the two links divided by 2. For components ...

There are two functions commonly denoted mu, each of which is defined in terms of integrals. Another unrelated mathematical function represented using the Greek letter mu is ...