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A triple (a,b,c) of positive integers satisfying a<b<c is said to be harmonic if 1/a+1/c=2/b. In particular, such a triple is harmonic if the reciprocals of its terms form an ...

Formulas obtained from differentiating Newton's forward difference formula, where R_n^'=h^nf^((n+1))(xi)d/(dp)(p; n+1)+h^(n+1)(p; n+1)d/(dx)f^((n+1))(xi), (n; k) is a ...

The prime distance pd(n) of a nonnegative integer n is the absolute difference between n and the nearest prime. It is therefore true that pd(p)=0 for primes p. The first few ...

The above two figures are rearrangements of each other, with the corresponding triangles and polyominoes having the same areas. Nevertheless, the bottom figure has an area ...

Every even number is the difference of two consecutive primes in infinitely many ways (Dickson 2005, p. 424). If true, taking the difference 2, this conjecture implies that ...

A projection matrix P is an n×n square matrix that gives a vector space projection from R^n to a subspace W. The columns of P are the projections of the standard basis ...

An operator A^~ such that A^~^2=A^~ or an element of an algebra x such that x^2=x.

A basis, form, function, etc., in two or more variables is said to be multilinear if it is linear in each variable separately.

An operator in logic which returns either true or false.

An operator definition of a function. A Rodrigues formula may be converted into a Schläfli integral.