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There are several q-analogs of the cosine function. The two natural definitions of the q-cosine defined by Koekoek and Swarttouw (1998) are given by cos_q(z) = ...

A prime triplet is a prime constellation of the form (p, p+2, p+6), (p, p+4, p+6), etc. Hardy and Wright (1979, p. 5) conjecture, and it seems almost certain to be true, that ...

The double factorial of a positive integer n is a generalization of the usual factorial n! defined by n!!={n·(n-2)...5·3·1 n>0 odd; n·(n-2)...6·4·2 n>0 even; 1 n=-1,0. (1) ...

Given a rectangle having sides in the ratio 1:phi, the golden ratio phi is defined such that partitioning the original rectangle into a square and new rectangle results in a ...

The Somos sequences are a set of related symmetrical recurrence relations which, surprisingly, always give integers. The Somos sequence of order k, or Somos-k sequence, is ...

A unigraphic graph (or simply a "unigraph") is a graph that is isomorphic to every graph having that degree sequence. All graphs on four are fewer vertices are unigraphic. ...

The homomorphism S which, according to the snake lemma, permits construction of an exact sequence (1) from the above commutative diagram with exact rows. The homomorphism S ...

A sequence of functions {f_n}, n=1, 2, 3, ... is said to be uniformly convergent to f for a set E of values of x if, for each epsilon>0, an integer N can be found such that ...

A cactus graph, sometimes also called a cactus tree, a mixed Husimi tree, or a polygonal cactus with bridges, is a connected graph in which any two graph cycles have no edge ...

A Gaussian integer is a complex number a+bi where a and b are integers. The Gaussian integers are members of the imaginary quadratic field Q(sqrt(-1)) and form a ring often ...