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The Wallis formula follows from the infinite product representation of the sine sinx=xproduct_(n=1)^infty(1-(x^2)/(pi^2n^2)). (1) Taking x=pi/2 gives ...

The asymptotic form of the n-step Bernoulli distribution with parameters p and q=1-p is given by P_n(k) = (n; k)p^kq^(n-k) (1) ∼ 1/(sqrt(2pinpq))e^(-(k-np)^2/(2npq)) (2) ...

The modern definition of the q-hypergeometric function is _rphi_s[alpha_1,alpha_2,...,alpha_r; beta_1,...,beta_s;q,z] ...

The Riemann zeta function is an extremely important special function of mathematics and physics that arises in definite integration and is intimately related with very deep ...

The circumcircle is a triangle's circumscribed circle, i.e., the unique circle that passes through each of the triangle's three vertices. The center O of the circumcircle is ...

In two dimensions, there are two periodic circle packings for identical circles: square lattice and hexagonal lattice. In 1940, Fejes Tóth proved that the hexagonal lattice ...

The (upper) vertex independence number of a graph, often called simply "the" independence number, is the cardinality of the largest independent vertex set, i.e., the size of ...

An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an ...

The Barnette-Bosák-Lederberg graph is a graph on 38 vertices which is the smallest known example of a planar 3-connected nonhamiltonian graph, i.e., the smallest known ...

A Boolean algebra is a mathematical structure that is similar to a Boolean ring, but that is defined using the meet and join operators instead of the usual addition and ...