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|_n]!={n! for n>=0; ((-1)^(-n-1))/((-n-1)!) for n<0. (1) The Roman factorial arises in the definition of the harmonic logarithm and Roman coefficient. It obeys the identities ...

A powerful numerical integration technique which uses k refinements of the extended trapezoidal rule to remove error terms less than order O(N^(-2k)). The routine advocated ...

The root separation (or zero separation) of a polynomial P(x) with roots r_1, r_2, ... is defined by Delta(P)=min_(i!=j)|r_i-r_j|. There are lower bounds on how close two ...

Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...

Let sum_(k=1)^(infty)u_k be a series with positive terms, and let rho=lim_(k->infty)u_k^(1/k). 1. If rho<1, the series converges. 2. If rho>1 or rho=infty, the series ...

The nth roots of unity are roots e^(2piik/n) of the cyclotomic equation x^n=1, which are known as the de Moivre numbers. The notations zeta_k, epsilon_k, and epsilon_k, where ...

A rotation group is a group in which the elements are orthogonal matrices with determinant 1. In the case of three-dimensional space, the rotation group is known as the ...

For algebraic alpha |alpha-p/q|<1/(q^(2+epsilon)), with epsilon>0, has finitely many solutions. Klaus Roth received a Fields medal for this result.

If n>19, there exists a Poulet number between n and n^2. The theorem was proved in 1965.

A rotor is a convex figure that can be rotated inside a polygon (or polyhedron) while always touching every side (or face). The least area rotor in a square is the Reuleaux ...