Search Results for ""

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 ...

As shown by Morse and Feshbach (1953), the Helmholtz differential equation is separable in confocal paraboloidal coordinates.

As shown by Morse and Feshbach (1953) and Arfken (1970), the Helmholtz differential equation is separable in oblate spheroidal coordinates.

As shown by Morse and Feshbach (1953) and Arfken (1970), the Helmholtz differential equation is separable in prolate spheroidal coordinates.

The Struve function, denoted H_n(z) or occasionally H_n(z), is defined as H_nu(z)=(1/2z)^(nu+1)sum_(k=0)^infty((-1)^k(1/2z)^(2k))/(Gamma(k+3/2)Gamma(k+nu+3/2)), (1) where ...

Connecting the centers of touching spheres in a three-dimensional Apollonian gasket by edges given a graph known as the Apollonian network. This process is illustrated above ...

An order-n Costas array is a permutation on {1,...,n} such that the distances in each row of the triangular difference table are distinct. For example, the permutation ...

A polygonal number is a type of figurate number that is a generalization of triangular, square, etc., to an n-gon for n an arbitrary positive integer. The above diagrams ...

Differential Equations

The Latin prefix quadri- is used to indicate the number 4, for example, quadrilateral, quadrant, etc. However, it also very commonly used to denote objects involving the ...