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A reflection relation is a functional equation relating f(-x) to f(x), or more generally, f(a-x) to f(x). Perhaps the best known example of a reflection formula is the gamma ...

The Riemann sphere, also called the extended complex plane, is a one-dimensional complex manifold C^* (C-star) which is the one-point compactification of the complex numbers ...

Given a map f:S->T between sets S and T, the map g:T->S is called a right inverse to f provided that f degreesg=id_T, that is, composing f with g from the right gives the ...

Rodrigues' rotation formula gives an efficient method for computing the rotation matrix R in SO(3) corresponding to a rotation by an angle theta about a fixed axis specified ...

The Rogers mod 14 identities are a set of three Rogers-Ramanujan-like identities given by A(q) = sum_(n=0)^(infty)(q^(n^2))/((q;q)_n(q;q^2)_n) (1) = ...

A generalization of the binomial coefficient whose notation was suggested by Knuth, |_n; k]=(|_n]!)/(|_k]!|_n-k]!), (1) where |_n] is a Roman factorial. The above expression ...

The nth roots of unity are roots e^(2piik/n) of the cyclotomic equation x^n=1, which are known as the de Moivre numbers. The notations zeta_k, epsilon_k, and epsilon_k, where ...

The semigroup algebra K[S], where K is a field and S a semigroup, is formally defined in the same way as the group algebra K[G]. Similarly, a semigroup ring R[S] is a ...

A short exact sequence of groups A, B, and C is given by two maps alpha:A->B and beta:B->C and is written 0->A->B->C->0. (1) Because it is an exact sequence, alpha is ...

Let A be an n×n matrix over a field F. Using the three elementary row and column operations over elements in the field, the n×n matrix xI-A with entries from the principal ...