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A mathematical procedure for finding the best-fitting curve to a given set of points by minimizing the sum of the squares of the offsets ("the residuals") of the points from ...

The Legendre polynomials, sometimes called Legendre functions of the first kind, Legendre coefficients, or zonal harmonics (Whittaker and Watson 1990, p. 302), are solutions ...

The fraction of odd values of the partition function P(n) is roughly 50%, independent of n, whereas odd values of Q(n) occur with ever decreasing frequency as n becomes ...

If there is an integer 0<x<p such that x^2=q (mod p), (1) i.e., the congruence (1) has a solution, then q is said to be a quadratic residue (mod p). Note that the trivial ...

Riemann defined the function f(x) by f(x) = sum_(p^(nu)<=x; p prime)1/nu (1) = sum_(n=1)^(|_lgx_|)(pi(x^(1/n)))/n (2) = pi(x)+1/2pi(x^(1/2))+1/3pi(x^(1/3))+... (3) (Hardy ...

A number is said to be squarefree (or sometimes quadratfrei; Shanks 1993) if its prime decomposition contains no repeated factors. All primes are therefore trivially ...

The Catalan numbers on nonnegative integers n are a set of numbers that arise in tree enumeration problems of the type, "In how many ways can a regular n-gon be divided into ...

A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path ...

The word "number" is a general term which refers to a member of a given (possibly ordered) set. The meaning of "number" is often clear from context (i.e., does it refer to a ...

A graph is said to be regular of degree r if all local degrees are the same number r. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, ...