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A circle that in internally tangent to two sides of a triangle and to the circumcircle is called a mixtilinear incircle. There are three mixtilinear incircles, one ...

The symbol tau (the lower case Greek letter tau) has many common uses in mathematics, as summarized in the following table. 1. tau(n) is an alternate notation for the divisor ...

A Liouville number is a transcendental number which has very close rational number approximations. An irrational number beta is called a Liouville number if, for each n, ...

Any bivariate distribution function with marginal distribution functions F and G satisfies max{F(x)+G(y)-1,0}<=H(x,y)<=min{F(x),G(y)}.

The third-order ordinary differential equation y^(''')+alphayy^('')+beta(1-y^('2))=0.

The Fourier transform of e^(-k_0|x|) is given by F_x[e^(-k_0|x|)](k)=int_(-infty)^inftye^(-k_0|x|)e^(-2piikx)dx = ...

f(z)=k/((cz+d)^r)f((az+b)/(cz+d)) where I[z]>0.

SNTP(n) is the smallest prime such that p#-1, p#, or p#+1 is divisible by n, where p# is the primorial of p. Ashbacher (1996) shows that SNTP(n) only exists 1. If there are ...

The wave equation in prolate spheroidal coordinates is del ...

The wave equation in oblate spheroidal coordinates is del ^2Phi+k^2Phi=partial/(partialxi_1)[(xi_1^2+1)(partialPhi)/(partialxi_1)] ...