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A plot of a function expressed in polar coordinates, with radius r as a function of angle theta. Polar plots can be drawn in the Wolfram Language using PolarPlot[r, {t, tmin, ...

A prime factorization algorithm also known as Pollard Monte Carlo factorization method. There are two aspects to the Pollard rho factorization method. The first is the idea ...

The probability density function (PDF) P(x) of a continuous distribution is defined as the derivative of the (cumulative) distribution function D(x), D^'(x) = ...

The pseudosquare L_p modulo the odd prime p is the least nonsquare positive integer that is congruent to 1 (mod 8) and for which the Legendre symbol (L_p/q)=1 for all odd ...

The sample variance m_2 (commonly written s^2 or sometimes s_N^2) is the second sample central moment and is defined by m_2=1/Nsum_(i=1)^N(x_i-m)^2, (1) where m=x^_ the ...

Let N samples be taken from a population with central moments mu_n. The sample variance m_2 is then given by m_2=1/Nsum_(i=1)^N(x_i-m)^2, (1) where m=x^_ is the sample mean. ...

For every positive integer n, there exists a circle in the plane having exactly n lattice points on its circumference. The theorem is based on the number r(n) of integral ...

The Seidel-Entringer-Arnold triangle is the number triangle consisting of the Entringer numbers E_(n,k) arranged in "ox-plowing" order, ...

The logarithmic integral is defined as the Cauchy principal value li(x) = PVint_0^x(dt)/(lnt) (1) = ...

Ramanujan's Dirichlet L-series is defined as f(s)=sum_(n=1)^infty(tau(n))/(n^s), (1) where tau(n) is the tau function. Note that the notation F(s) is sometimes used instead ...