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Given a unit line segment [0,1], pick two points at random on it. Call the first point x_1 and the second point x_2. Find the distribution of distances d between points. The ...

Series reversion is the computation of the coefficients of the inverse function given those of the forward function. For a function expressed in a series with no constant ...

Simpson's rule is a Newton-Cotes formula for approximating the integral of a function f using quadratic polynomials (i.e., parabolic arcs instead of the straight line ...

A universal differential equation (UDE) is a nontrivial differential-algebraic equation with the property that its solutions approximate to arbitrary accuracy any continuous ...

The generalized Riemann hypothesis conjectures that neither the Riemann zeta function nor any Dirichlet L-series has a zero with real part larger than 1/2. Compare with ...

e^(izcostheta)=sum_(n=-infty)^inftyi^nJ_n(z)e^(intheta), where J_n(z) is a Bessel function of the first kind. The identity can also be written ...

The Longuet-Higgins point is the radical center of the circles centered at the vertices A, B, and C of a reference triangle with respective radii b+c, c+a, and a+b. It has ...

An asymptotic series is a series expansion of a function in a variable x which may converge or diverge (Erdélyi 1987, p. 1), but whose partial sums can be made an arbitrarily ...

The complete elliptic integral of the first kind K(k), illustrated above as a function of the elliptic modulus k, is defined by K(k) = F(1/2pi,k) (1) = ...

The hypersine (n-dimensional sine function) is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the ...