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The odd part Od(n) of a positive integer n is defined by Od(n)=n/(2^(b(n))), where b(n) is the exponent of the exact power of 2 dividing n. Od(n) is therefore the product of ...

Physicists and engineers use the phrase "order of magnitude" to refer to the smallest power of ten needed to represent a quantity. Two quantities A and B which are within ...

Let 0<p_1<p_2<... be integers and suppose that there exists a lambda>1 such that p_(j+1)/p_j>lambda for j=1, 2, .... Suppose that for some sequence of complex numbers {a_j} ...

If P(z) is a power series which is regular for |z|<=1 except for m poles within this circle and except for z=+1, at which points the function is assumed continuous when only ...

Let A be a finite-dimensional power-associative algebra, then A is the vector space direct sum A=A_(11)+A_(10)+A_(01)+A_(00), where A_(ij), with i,j=0,1 is the subspace of A ...

A group that coincides with its commutator subgroup. If G is a non-Abelian group, its commutator subgroup is a normal subgroup other than the trivial group. It follows that ...

The statistics h_(r,s,...) defined such that <h_(r,s,...)>=mu_rmu_s..., where mu_r is a central moment. These statistics generalize h-statistics and were originally called ...

The highest power in a univariate polynomial is known as its degree, or sometimes "order." For example, the polynomial P(x)=a_nx^n+...+a_2x^2+a_1x+a_0 is of degree n, denoted ...

The power polynomials x^n are an associated Sheffer sequence with f(t)=t, (1) giving generating function sum_(k=0)^inftyx^kt^k=1/(1-tx) (2) and exponential generating ...

The radical lines of three circles are concurrent in a point known as the radical center (also called the power center). This theorem was originally demonstrated by Monge ...