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The Kiepert center X_(115) (center of the Kiepert hyperbola) lies on the nine-point circle. The Kiepert antipode is the antipode of this point on nine-point circle. It has ...
Knuth's series is given by S = sum_(k=1)^(infty)((k^k)/(k!e^k)-1/(sqrt(2pik))) (1) = -2/3-1/(sqrt(2pi))zeta(1/2) (2) = -0.08406950872765599646... (3) (OEIS A096616), where ...
The forward and inverse Kontorovich-Lebedev transforms are defined by K_(ix)[f(t)] = int_0^inftyK_(ix)(t)f(t)dt (1) K_(ix)^(-1)[g(t)] = ...
An equation proposed by Lambert (1758) and studied by Euler in 1779. x^alpha-x^beta=(alpha-beta)vx^(alpha+beta). (1) When alpha->beta, the equation becomes lnx=vx^beta, (2) ...
Let ||f|| be the supremum of |f(x)|, a real-valued function f defined on (0,infty). If f is twice differentiable and both f and f^('') are bounded, Landau (1913) showed that ...
Given a function of the form y=a+blnx, (1) the coefficients can be found from least squares fitting as b = ...
In practice, the vertical offsets from a line (polynomial, surface, hyperplane, etc.) are almost always minimized instead of the perpendicular offsets. This provides a ...
Legendre-Gauss quadrature is a numerical integration method also called "the" Gaussian quadrature or Legendre quadrature. A Gaussian quadrature over the interval [-1,1] with ...
A local Banach algebra is a normed algebra A=(A,|·|_A) which satisfies the following properties: 1. If x in A and f is an analytic function on a neighborhood of the spectrum ...
The Longuet-Higgins circle is the radical circle 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. Its ...
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