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A generalization of the binomial coefficient whose notation was suggested by Knuth, |_n; k]=(|_n]!)/(|_k]!|_n-k]!), (1) where |_n] is a Roman factorial. The above expression ...

|_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 ...

For a set of n numbers or values of a discrete distribution x_i, ..., x_n, the root-mean-square (abbreviated "RMS" and sometimes called the quadratic mean), is the square ...

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 ...

Rosser's rule states that every Gram block contains the expected number of roots, which appears to be true for computable Gram blocks. Rosser et al. (1969) expressed a belief ...

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 ...

Hoffman (1998, p. 90) calls the sum of the exponents in the prime factorization of a number its roundness. The first few values for n=1, 2, ... are 0, 1, 1, 2, 1, 2, 1, 3, 2, ...

Rubik's Clock is a puzzle consisting of 18 small clocks, 14 of which are independent, each of which may be set to any 12-hour position. There are therefore 12^(14) possible ...

Let K subset= C be compact, let f be analytic on a neighborhood of K, and let P subset= C^*\K contain at least one point from each connected component of C^*\K. Then for any ...