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int_0^inftycos(2zt)sech(pit)dt=1/2sechz for |I[z]|<pi/2. A related integral is int_0^inftycosh(2zt)sech(pit)dt=1/2secz for |R[z]|<pi/2.

For a point y in Y, with f(y)=x, the ramification index of f at y is a positive integer e_y such that there is some open neighborhood U of y so that x has only one preimage ...

A type of cusp as illustrated above for the curve x^4+x^2y^2-2x^2y-xy^2+y^2=0.

The fractal-like figure obtained by performing the same iteration as for the Mandelbrot set, but adding a random component R, z_(n+1)=z_n^2+c+R. In the above plot, ...

A random composition of a number n in k parts is one of the (n+k-1; n) possible compositions of n, where (n; k) is a binomial coefficient. A random composition can be given ...

A Young tableau chosen at random from those having a given shape. A random tableau can be generated by RandomTableau[shape] in the Wolfram Language package Combinatorica` . ...

Let V and W be vector spaces over a field F, and let T:V->W be a linear transformation. Assuming the dimension of V is finite, then dim(V)=dim(Ker(T))+dim(Im(T)), where ...

The ratio of two numbers r and s is written r/s, where r is the numerator and s is the denominator. The ratio of r to s is equivalent to the quotient r/s. Betting odds ...

A synonym for integer. The word "rational" is sometimes used for emphasis to distinguish it from other types of "integers" such as cyclotomic integers, Eisenstein integers, ...

A rational quadrilateral is a quadrilateral for which the sides, polygon diagonals, and area are rational. The simplest case has sides a=52, b=25, c=39, and d=60, polygon ...