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A vector is formally defined as an element of a vector space. In the commonly encountered vector space R^n (i.e., Euclidean n-space), a vector is given by n coordinates and ...

The Wigner 3j-symbols (j_1 j_2 j_3; m_1 m_2 m_3), also known as "3j symbols" (Messiah 1962, p. 1056) or Wigner coefficients (Shore and Menzel 1968, p. 275) are quantities ...

The Zermelo-Fraenkel axioms are the basis for Zermelo-Fraenkel set theory. In the following (Jech 1997, p. 1), exists stands for exists, forall means for all, in stands for ...

A p-adic number is an extension of the field of rationals such that congruences modulo powers of a fixed prime p are related to proximity in the so called "p-adic metric." ...

A q-series is series involving coefficients of the form (a;q)_n = product_(k=0)^(n-1)(1-aq^k) (1) = product_(k=0)^(infty)((1-aq^k))/((1-aq^(k+n))) (2) = ...

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

A problem posed by L. Collatz in 1937, also called the 3x+1 mapping, 3n+1 problem, Hasse's algorithm, Kakutani's problem, Syracuse algorithm, Syracuse problem, Thwaites ...

The m×n knight graph is a graph on mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a knight (which may ...

A prime gap of length n is a run of n-1 consecutive composite numbers between two successive primes. Therefore, the difference between two successive primes p_k and p_(k+1) ...

In mathematics, a knot is defined as a closed, non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., the ...