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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 ...

If x_0 is an ordinary point of the ordinary differential equation, expand y in a Taylor series about x_0. Commonly, the expansion point can be taken as x_0=0, resulting in ...

The most common "sine integral" is defined as Si(z)=int_0^z(sint)/tdt (1) Si(z) is the function implemented in the Wolfram Language as the function SinIntegral[z]. Si(z) is ...

A tag system in which a list of n tag rules (each of a special form) is applied to a system in sequential order and then starting again from the first rule. In a cyclic tag ...

The wave equation in prolate spheroidal coordinates is del ...

The Weingarten equations express the derivatives of the normal vector to a surface using derivatives of the position vector. Let x:U->R^3 be a regular patch, then the shape ...

The following integral transform relationship, known as the Abel transform, exists between two functions f(x) and g(t) for 0<alpha<1, f(x) = int_0^x(g(t)dt)/((x-t)^alpha) (1) ...

A set partition of a set S is a collection of disjoint subsets of S whose union is S. The number of partitions of the set {k}_(k=1)^n is called a Bell number.

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 ...

Presburger arithmetic is the first-order theory of the natural numbers containing addition but no multiplication. It is therefore not as powerful as Peano arithmetic. ...