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H_n^((2))(z)=J_n(z)-iY_n(z), (1) where J_n(z) is a Bessel function of the first kind and Y_n(z) is a Bessel function of the second kind. Hankel functions of the second kind ...

The equation defining Killing vectors. L_Xg_(ab)=X_(a;b)+X_(b;a)=2X_((a;b))=0, where L is the Lie derivative and X_(b;a) is a covariant derivative.

The partial differential equation u_t+u_x-6uu_x-u_(txx)=0.

A recurrence equation (also called a difference equation) is the discrete analog of a differential equation. A difference equation involves an integer function f(n) in a form ...

In two-dimensional bipolar coordinates, Laplace's equation is ((coshv-cosu)^2)/(a^2)((partialF^2)/(partialu^2)+(partialF^2)/(partialv^2))=0, which simplifies to ...

The logistic equation (sometimes called the Verhulst model or logistic growth curve) is a model of population growth first published by Pierre Verhulst (1845, 1847). The ...

There are two types of functions known as Hankel functions. The more common one is a complex function (also called a Bessel function of the third kind, or Weber Function) ...

An ordinary differential equation of the form x^my^'=f(x,y), where m is a positive integer, f is analytic at x=y=0, f(0,0)=0, and f_y^'(0,0)!=0. Zwillinger (1997, p. 120), ...

A partial differential diffusion equation of the form (partialU)/(partialt)=kappadel ^2U. (1) Physically, the equation commonly arises in situations where kappa is the ...

Special functions which arise as solutions to second order ordinary differential equations are commonly said to be "of the first kind" if they are nonsingular at the origin, ...