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Comprehensive encyclopedia of mathematics with 13,000 detailed entries. Continually updated, extensively illustrated, and with interactive examples.

delta(x-t)=sum_(n=0)^inftyphi_n(x)phi_n(t), where delta(x) is the delta function.

The common logarithm is the logarithm to base 10. The notation logx is used by physicists, engineers, and calculator keypads to denote the common logarithm. However, ...

The square torus is the quotient of the plane by the integer lattice.

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The axiom of Zermelo-Fraenkel set theory which asserts that sets formed by the same elements are equal, forall x(x in a=x in b)=>a=b. Note that some texts (e.g., Devlin ...

In the study of non-associative algebra, there are at least two different notions of what the half-Bol identity is. Throughout, let L be an algebraic loop and let x, y, and z ...

Overdamped simple harmonic motion is a special case of damped simple harmonic motion x^..+betax^.+omega_0^2x=0, (1) in which beta^2-4omega_0^2>0. (2) Therefore ...

The symbol RadicalBox[x, n] used to indicate a root is called a radical, or sometimes a surd. The expression RadicalBox[x, n] is therefore read "x radical n," or "the nth ...

Let the two-dimensional cylinder function be defined by f(x,y)={1 for r<R; 0 for r>R. (1) Then the Radon transform is given by ...