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The r-Hofstadter triangle of a given triangle DeltaABC is perspective to DeltaABC, and the perspector is called the Hofstadter point. The triangle center function is ...

A triangle center alpha:beta:gamma is called a major triangle center if the triangle center function alpha=f(a,b,c,A,B,C) is a function of angle A alone, and therefore beta ...

The map-Airy distribution is a statistical distribution having probability density function and distribution function P(x) = 2e^(-2x^3/3)[xAi(x^2)-Ai^'(x^2)] (1) D(x) = (2) ...

The Radon-Nikodym theorem asserts that any absolutely continuous complex measure lambda with respect to some positive measure mu (which could be Lebesgue measure or Haar ...

The nth Ramanujan prime is the smallest number R_n such that pi(x)-pi(x/2)>=n for all x>=R_n, where pi(x) is the prime counting function. In other words, there are at least n ...

Let phi(n) be any function, say analytic or integrable. Then int_0^inftyx^(s-1)sum_(k=0)^infty(-1)^kx^kphi(k)dx=(piphi(-s))/(sin(spi)) (1) and ...

Let f be a real-valued, continuous, and strictly increasing function on [0,c] with c>0. If f(0)=0, a in [0,c], and b in [0,f(c)], then int_0^af(x)dx+int_0^bf^(-1)(x)dx>=ab, ...

A continuous distribution defined on the range x in [0,2pi) with probability density function P(x)=(e^(bcos(x-a)))/(2piI_0(b)), (1) where I_0(x) is a modified Bessel function ...

Legendre's formula counts the number of positive integers less than or equal to a number x which are not divisible by any of the first a primes, (1) where |_x_| is the floor ...

In many computer languages (such as FORTRAN or the Wolfram Language), the common residue of b (mod m) is written mod(b, m) (FORTRAN) or Mod[b, m] (Wolfram Language). The ...