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Given a pair of orthologic triangles, the point where the perpendiculars from the vertices of the first to the sides of the second concur and the point where the ...

The second-order ordinary differential equation x^2(d^2y)/(dx^2)+x(dy)/(dx)-(x^2+n^2)y=0. (1) The solutions are the modified Bessel functions of the first and second kinds, ...

The second-order ordinary differential equation y^('')+[(alphaeta)/(1+eta)+(betaeta)/((1+eta)^2)+gamma]y=0, where eta=e^(deltax).

Another name for the confluent hypergeometric function of the second kind, defined by where Gamma(x) is the gamma function and _1F_1(a;b;z) is the confluent hypergeometric ...

The second-order ordinary differential equation y^('')+[alpha/(cosh^2(ax))+betatanh(ax)+gamma]y=0.

A subset E of a topological space S is said to be nonmeager if E is of second category in S, i.e., if E cannot be written as the countable union of subsets which are nowhere ...

A theorem sometimes called "Euclid's first theorem" or Euclid's principle states that if p is a prime and p|ab, then p|a or p|b (where | means divides). A corollary is that ...

A pair of overdots placed over a symbol, as in x^.., most commonly used to denote a second derivative with respect to time, i.e., x^..=d^2x/dt^2.

For n players, n-1 games are needed to fairly determine first place, and n-1+lg(n-1) are needed to fairly determine first and second place.

If one event can occur in m ways and a second can occur independently of the first in n ways, then the two events can occur in mn ways.