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Extend Hilbert's inequality by letting p,q>1 and 1/p+1/q>=1, (1) so that 0<lambda=2-1/p-1/q<=1. (2) Levin (1937) and Stečkin (1949) showed that (3) and ...

Homogeneous coordinates (x_1,x_2,x_3) of a finite point (x,y) in the plane are any three numbers for which (x_1)/(x_3)=x (1) (x_2)/(x_3)=y. (2) Coordinates (x_1,x_2,0) for ...

A homogeneous space M is a space with a transitive group action by a Lie group. Because a transitive group action implies that there is only one group orbit, M is isomorphic ...

The hyperfactorial (Sloane and Plouffe 1995) is the function defined by H(n) = K(n+1) (1) = product_(k=1)^(n)k^k, (2) where K(n) is the K-function. The hyperfactorial is ...

For an n×n matrix, let S denote any permutation e_1, e_2, ..., e_n of the set of numbers 1, 2, ..., n, and let chi^((lambda))(S) be the character of the symmetric group ...

Given a sequence of real numbers a_n, the infimum limit (also called the limit inferior or lower limit), written lim inf and pronounced 'lim-inf,' is the limit of ...

A polynomial of the form f(x)=a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0 having coefficients a_i that are all integers. An integer polynomial gives integer values for all integer ...

A partially ordered set P=(X,<=) is an interval order if it is isomorphic to some set of intervals on the real line ordered by left-to-right precedence. Formally, P is an ...

The inverse tangent is the multivalued function tan^(-1)z (Zwillinger 1995, p. 465), also denoted arctanz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 311; ...

"The" Jacobi identity is a relationship [A,[B,C]]+[B,[C,A]]+[C,[A,B]]=0,, (1) between three elements A, B, and C, where [A,B] is the commutator. The elements of a Lie algebra ...