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The beta function B(p,q) is the name used by Legendre and Whittaker and Watson (1990) for the beta integral (also called the Eulerian integral of the first kind). It is ...

sum_(k=0)^m(phi_k(x)phi_k(y))/(gamma_k)=(phi_(m+1)(x)phi_m(y)-phi_m(x)phi_(m+1)(y))/(a_mgamma_m(x-y),) (1) where phi_k(x) are orthogonal polynomials with weighting function ...

The ratio of a measure of the size of a "fit" to the size of a "residual."

A special function which is given by the logarithmic derivative of the gamma function (or, depending on the definition, the logarithmic derivative of the factorial). Because ...

A dual number is a number x+epsilony, where x,y in R and epsilon is a matrix with the property that epsilon^2=0 (such as epsilon=[0 1; 0 0]).

Handles and cross-handles are equivalent in the presence of a cross-cap.

erf(z) is the "error function" encountered in integrating the normal distribution (which is a normalized form of the Gaussian function). It is an entire function defined by ...

A special case of the Artin L-function for the polynomial x^2+1. It is given by L(s)=product_(p odd prime)1/(1-chi^-(p)p^(-s)), (1) where chi^-(p) = {1 for p=1 (mod 4); -1 ...

The first quadratic nonresidue mod p of a number is always less than 3(lnp)^2/2 (Wedeniwski 2001).

A phrase used by Tukey to describe data points which are outside the outer fences.