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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 ...

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.

An equichordal point is a point p for which all the chords of a curve C passing through p are of the same length. In other words, p is an equichordal point if, for every ...

Maxwell's equations are the system of partial differential equations describing classical electromagnetism and therefore of central importance in physics. In the so-called ...

A weak Riemannian metric on a smooth manifold M is a (0,2) tensor field g which is both a weak pseudo-Riemannian metric and positive definite. In a very precise way, the ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...

A distribution which arises in the study of integer spin particles in physics, P(k)=(k^s)/(e^(k-mu)-1). (1) Its integral is given by int_0^infty(k^sdk)/(e^(k-mu)-1) = ...

The Lerch transcendent is generalization of the Hurwitz zeta function and polylogarithm function. Many sums of reciprocal powers can be expressed in terms of it. It is ...