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A series which is not convergent. Series may diverge by marching off to infinity or by oscillating. Divergent series have some curious properties. For example, rearranging ...

The divided difference f[x_0,x_1,x_2,...,x_n], sometimes also denoted [x_0,x_1,x_2,...,x_n] (Abramowitz and Stegun 1972), on n+1 points x_0, x_1, ..., x_n of a function f(x) ...

In order to find integers x and y such that x^2=y^2 (mod n) (1) (a modified form of Fermat's factorization method), in which case there is a 50% chance that GCD(n,x-y) is a ...

_3F_2[n,-x,-y; x+n+1,y+n+1] =Gamma(x+n+1)Gamma(y+n+1)Gamma(1/2n+1)Gamma(x+y+1/2n+1) ×Gamma(n+1)Gamma(x+y+n+1)Gamma(x+1/2n+1)Gamma(y+1/2n+1), (1) where _3F_2(a,b,c;d,e;z) is a ...

The term domain has (at least) three different meanings in mathematics. The term domain is most commonly used to describe the set of values D for which a function (map, ...

For a graph G and a subset S of the vertex set V(G), denote by N_G[S] the set of vertices in G which are in S or adjacent to a vertex in S. If N_G[S]=V(G), then S is said to ...

The Fibonacci number F_(n+1) gives the number of ways for 2×1 dominoes to cover a 2×n checkerboard, as illustrated in the diagrams above (Dickau). The numbers of domino ...

The Doob graph D(m,n) is the graph given by the graph Cartesian product of m>=1 copies of the Shrikhande graph with a Hamming graph H(n,4). Doob graphs are distance-regular ...

Dots and boxes is a two-person game based on a rectangular lattice of points. Each player, in turn, draws a horizontal or vertical line connecting two adjacent points. ...

A set of positive integers is double-free if, for any integer x, the set {x,2x} !subset= S (or equivalently, x in S implies 2x not in S). For example, of the subsets of ...