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

The Helmholtz differential equation in spherical coordinates is separable. In fact, it is separable under the more general condition that k^2 is of the form ...

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 hemicube, which might also be called the square hemiprism, is a simple solid that serves as an example of one of the two topological classes of convex hexahedron having 7 ...

When the elongated square pyramid with unit edge lengths (i.e., an equilateral obelisk) is truncated by a plane passing through opposite corners of its square base and the ...

Let H be a heptagon with seven vertices given in cyclic order inscribed in a conic. Then the Pascal lines of the seven hexagons obtained by omitting each vertex of H in turn ...

A number which is simultaneously a heptagonal number Hep_n and hexagonal number Hex_m. Such numbers exist when 1/2n(5n-3)=m(2m-1). (1) Completing the square and rearranging ...

A number which is simultaneously a heptagonal number H_n and pentagonal number P_m. Such numbers exist when 1/2n(5n-3)=1/2m(3m-1). (1) Completing the square and rearranging ...

A number which is simultaneously a heptagonal number H_n and square number S_m. Such numbers exist when 1/2n(5n-3)=m^2. (1) Completing the square and rearranging gives ...

A number which is simultaneously a heptagonal number H_n and triangular number T_m. Such numbers exist when 1/2n(5n-3)=1/2m(m+1). (1) Completing the square and rearranging ...