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The scale factors are h_u=h_v=sqrt(u^2+v^2), h_theta=uv and the separation functions are f_1(u)=u, f_2(v)=v, f_3(theta)=1, given a Stäckel determinant of S=u^2+v^2. The ...

In conical coordinates, Laplace's equation can be written ...

Spinor fields describing particles of zero rest mass satisfy the so-called zero rest mass equations. Examples of zero rest mass particles include the neutrino (a fermion) and ...

Euler (1772ab) conjectured that there are no positive integer solutions to the quartic Diophantine equation A^4=B^4+C^4+D^4. This conjecture was disproved by Elkies (1988), ...

The smallest nontrivial taxicab number, i.e., the smallest number representable in two ways as a sum of two cubes. It is given by 1729=1^3+12^3=9^3+10^3. The number derives ...

An inhomogeneous linear ordinary differential equation with constant coefficients is an ordinary differential equation in which coefficients are constants (i.e., not ...

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

A homogeneous linear ordinary differential equation with constant coefficients is an ordinary differential equation in which coefficients are constants (i.e., not functions), ...

To solve the system of differential equations (dx)/(dt)=Ax(t)+p(t), (1) where A is a matrix and x and p are vectors, first consider the homogeneous case with p=0. The ...

If one solution (y_1) to a second-order ordinary differential equation y^('')+P(x)y^'+Q(x)y=0 (1) is known, the other (y_2) may be found using the so-called reduction of ...