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On the surface of a sphere, attempt separation of variables in spherical coordinates by writing F(theta,phi)=Theta(theta)Phi(phi), (1) then the Helmholtz differential ...

Hermite-Gauss quadrature, also called Hermite quadrature, is a Gaussian quadrature over the interval (-infty,infty) with weighting function W(x)=e^(-x^2) (Abramowitz and ...

The second-order ordinary differential equation (d^2y)/(dx^2)-2x(dy)/(dx)+lambday=0. (1) This differential equation has an irregular singularity at infty. It can be solved ...

Let l(x) be an nth degree polynomial with zeros at x_1, ..., x_n. Then the fundamental Hermite interpolating polynomials of the first and second kinds are defined by ...

A hexagon is a six-sided polygon. Several special types of hexagons are illustrated above. In particular, a hexagon with vertices equally spaced around a circle and with all ...

The Hh-function is a function closely related to the normal distribution function. It can be defined using the auxilary functions Z(x) = 1/(sqrt(2pi))e^(-x^2/2) (1) Q(x) = ...

The Hofstadter ellipses are a family of triangle ellipses introduced by P. Moses in February 2005. The Hofstadter ellipse E(r) for parameter 0<r<1 is defined by the trilinear ...

Honaker's problem asks for all consecutive prime number triples (p,q,r) with p<q<r such that p|(qr+1). Caldwell and Cheng (2005) showed that the only Honaker triplets for ...

An improper integral is a definite integral that has either or both limits infinite or an integrand that approaches infinity at one or more points in the range of ...

The "complete" gamma function Gamma(a) can be generalized to the incomplete gamma function Gamma(a,x) such that Gamma(a)=Gamma(a,0). This "upper" incomplete gamma function is ...