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Darboux's formula is a theorem on the expansion of functions in infinite series and essentially consists of integration by parts on a specific integrand product of functions. ...

The Dedekind psi-function is defined by the divisor product psi(n)=nproduct_(p|n)(1+1/p), (1) where the product is over the distinct prime factors of n, with the special case ...

An embedding of a 1-sphere in a 3-manifold which exists continuously over the 2-disk also extends over the disk as an embedding. An alternate phrasing is that if a knot group ...

An algorithm which allows digits of a given number to be calculated without requiring the computation of earlier digits. The BBP formula for pi is the best-known such ...

A general quadratic Diophantine equation in two variables x and y is given by ax^2+cy^2=k, (1) where a, c, and k are specified (positive or negative) integers and x and y are ...

An illusion studied by the psychologist Walter Ehrenstein in which the sides of a square placed inside a pattern of concentric circles take an apparent curved shape. The name ...

The E_n(x) function is defined by the integral E_n(x)=int_1^infty(e^(-xt)dt)/(t^n) (1) and is given by the Wolfram Language function ExpIntegralE[n, x]. Defining t=eta^(-1) ...

The case of the Weierstrass elliptic function with invariants g_2=0 and g_3=1. The corresponding real half-period is given by omega_2 = (Gamma^3(1/3))/(4pi) (1) = ...

In predicate calculus, an existential formula is a prenex normal form formula (i.e., a formula written as a string of quantifiers and bound variables followed by a ...

The exponential transform is the transformation of a sequence a_1, a_2, ... into a sequence b_1, b_2, ... according to the equation ...