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In parabolic cylindrical coordinates, the scale factors are h_u=h_v=sqrt(u^2+v^2), h_z=1 and the separation functions are f_1(u)=f_2(v)=f_3(z)=1, giving Stäckel determinant ...

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 ...

The heptanacci numbers are a generalization of the Fibonacci numbers defined by H_0=0, H_1=1, H_2=1, H_3=2, H_4=4, H_5=8, H_6=16, and the recurrence relation ...

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 number which is simultaneously pentagonal and hexagonal. Let P_n denote the nth pentagonal number and H_m the mth hexagonal number, then a number which is both pentagonal ...

A hexahedral graph is a polyhedral graph on six vertices. There are seven distinct hexahedral graphs (illustrated above) which, through duality, correspond to seven convex ...

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) = ...

A minimal embedded surface discovered in 1992 consisting of a helicoid with a hole and handle (Science News 1992). It has the same topology as a punctured sphere with a ...