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X is a spherical t-design in E iff it is possible to exactly determine the average value on E of any polynomial f of degree at most t by sampling f at the points of X. In ...

A formula also known as the Legendre addition theorem which is derived by finding Green's functions for the spherical harmonic expansion and equating them to the generating ...

A Stoneham number is a number alpha_(b,c) of the form alpha_(b,c)=sum_(k=1)^infty1/(b^(c^k)c^k), where b,c>1 are relatively prime positive integers. Stoneham (1973) proved ...

The survival function describes the probability that a variate X takes on a value greater than a number x (Evans et al. 2000, p. 6). The survival function is therefore ...

A pair (M,omega), where M is a manifold and omega is a symplectic form on M. The phase space R^(2n)=R^n×R^n is a symplectic manifold. Near every point on a symplectic ...

If W is a k-dimensional subspace of a vector space V with inner product <,>, then it is possible to project vectors from V to W. The most familiar projection is when W is the ...

Let one grain of wheat be placed on the first square of a chessboard, two on the second, four on the third, eight on the fourth, etc. How many grains total are placed on an ...

The (unilateral) Z-transform of a sequence {a_k}_(k=0)^infty is defined as Z[{a_k}_(k=0)^infty](z)=sum_(k=0)^infty(a_k)/(z^k). (1) This definition is implemented in the ...

A lattice path from one point to another is p-good if it lies completely below the line y=(p-1)x. (1) Hilton and Pederson (1991) show that the number of p-good paths from (1, ...

A p-adic integer is a p-adic number of the form sum_(k=m)^(infty)a_kp^k, where m>=0, a_k are integers, and p is prime. It is sufficient to take a_k in the set {0,1,...,p-1}. ...