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To pick a random point on the surface of a unit sphere, it is incorrect to select spherical coordinates theta and phi from uniform distributions theta in [0,2pi) and phi in ...

An infinite sequence of positive integers a_i satisfying 1<=a_1<a_2<a_3<... (1) is an A-sequence if no a_k is the sum of two or more distinct earlier terms (Guy 1994). Such ...

Reciprocation is an incidence-preserving transformation in which points are transformed into their polars. A projective geometry-like duality principle holds for ...

The continuous Fourier transform is defined as f(nu) = F_t[f(t)](nu) (1) = int_(-infty)^inftyf(t)e^(-2piinut)dt. (2) Now consider generalization to the case of a discrete ...

The Lovász number theta(G) of a graph G, sometimes also called the theta function of G, was introduced by Lovász (1979) with the explicit goal of estimating the Shannon ...

The logarithm of the reciprocal of a number, equal to the negative of the logarithm of the number itself, cologx=log(1/x)=-logx.

A curve and its polar reciprocal with regard to the fixed conic have the same Halphen transformation.

The operator partial^_ is defined on a complex manifold, and is called the 'del bar operator.' The exterior derivative d takes a function and yields a one-form. It decomposes ...

Let alpha(x) be a step function with the jump j(x)=(N; x)p^xq^(N-x) (1) at x=0, 1, ..., N, where p>0,q>0, and p+q=1. Then the Krawtchouk polynomial is defined by ...

An approximation for the gamma function Gamma(z+1) with R[z]>0 is given by Gamma(z+1)=sqrt(2pi)(z+sigma+1/2)^(z+1/2)e^(-(z+sigma+1/2))sum_(k=0)^inftyg_kH_k(z), (1) where ...