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Expanding the Riemann zeta function about z=1 gives zeta(z)=1/(z-1)+sum_(n=0)^infty((-1)^n)/(n!)gamma_n(z-1)^n (1) (Havil 2003, p. 118), where the constants ...

The signed Stirling numbers of the first kind are variously denoted s(n,m) (Riordan 1980, Roman 1984), S_n^((m)) (Fort 1948, Abramowitz and Stegun 1972), S_n^m (Jordan 1950). ...

A strong pseudoprime to a base a is an odd composite number n with n-1=d·2^s (for d odd) for which either a^d=1 (mod n) (1) or a^(d·2^r)=-1 (mod n) (2) for some r=0, 1, ..., ...

A k-regular simple graph G on nu nodes is strongly k-regular if there exist positive integers k, lambda, and mu such that every vertex has k neighbors (i.e., the graph is a ...

Sylvester's four-point problem asks for the probability q(R) that four points chosen at random in a planar region R have a convex hull which is a quadrilateral (Sylvester ...

The tangent function is defined by tanx=(sinx)/(cosx), (1) where sinx is the sine function and cosx is the cosine function. The notation tgx is sometimes also used ...

Every planar graph (i.e., graph with graph genus 0) has an embedding on a torus. In contrast, toroidal graphs are embeddable on the torus, but not in the plane, i.e., they ...

N_phi(m) is the number of integers n for which the totient function phi(n)=m, also called the multiplicity of m (Guy 1994). Erdős (1958) proved that if a multiplicity occurs ...

Let G be an undirected graph, and let i denote the cardinal number of the set of externally active edges of a spanning tree T of G, j denote the cardinal number of the set of ...

Hilbert's problems are a set of (originally) unsolved problems in mathematics proposed by Hilbert. Of the 23 total appearing in the printed address, ten were actually ...