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The second-order ordinary differential equation satisfied by the Neumann polynomials O_n(x).

The second-order ordinary differential equation y^('')+[A+Bcos(2x)+Ccos(4x)]y=0.

A curve also known as the Gerono lemniscate. It is given by Cartesian coordinates x^4=a^2(x^2-y^2), (1) polar coordinates, r^2=a^2sec^4thetacos(2theta), (2) and parametric ...

The (circular) helicoid is the minimal surface having a (circular) helix as its boundary. It is the only ruled minimal surface other than the plane (Catalan 1842, do Carmo ...

Turing machines are defined by sets of rules that operate on four parameters: (state, tape cell color, operation, state). Let the states and tape cell colors be numbered and ...

A maze, also known as a labyrinth, as is a set of passages (with impermeable walls). The goal of the maze is to start at one given point and find a path through the passages ...

The quadrifolium is the 4-petalled rose curve having n=2. It has polar equation r=asin(2theta) (1) and Cartesian equation (x^2+y^2)^3=4a^2x^2y^2. (2) The area of the ...

The function defined by (1) (Heatley 1943; Abramowitz and Stegun 1972, p. 509), where _1F_1(a;b;z) is a confluent hypergeometric function of the first kind and Gamma(z) is ...

The operator representing the computation of a derivative, D^~=d/(dx), (1) sometimes also called the Newton-Leibniz operator. The second derivative is then denoted D^~^2, the ...

An indicial equation, also called a characteristic equation, is a recurrence equation obtained during application of the Frobenius method of solving a second-order ordinary ...