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A reduced root system is a root system R satisfying the additional property that, if alpha in R, then the only multiples of alpha in R are +/-alpha.

A function is termed regular iff it is analytic and single-valued throughout a region R.

For the Helmholtz differential equation to be separable in a coordinate system, the scale factors h_i in the Laplacian del ...

The Rutherford constant is a mathematical constant that arises in plasma physics and is defined by K_R = sqrt(2)int_(-1)^infty([R(x)]^2)/(S[x])dx (1) = 0.8227..., (2) where ...

A scalar is a one-component quantity that is invariant under rotations of the coordinate system.

A map f:R^n|->R which assigns each x a scalar function f(x).

Let P(1/x) be a linear functional acting according to the formula <P(1/x),phi> = Pint(phi(x))/xdx (1) = ...

A surface harmonic of degree l which is premultiplied by a factor r^l. Confusingly, solid harmonics are also known as "spherical harmonics" (Whittaker and Watson 1990, p. ...

The asymptotic series of the Airy function Ai(z) (and other similar functions) has a different form in different sectors of the complex plane.

A condition which, if true, guarantees that a result is also true. (However, the result may also be true if the condition is not met.) If a condition is both necessary and ...