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For |z|<1, product_(k=1)^infty(1+z^k)=product_(k=1)^infty(1-z^(2k-1))^(-1). (1) Both of these have closed form representation 1/2(-1;z)_infty, (2) where (a;q)_infty is a ...

An Euler number prime is an Euler number E_n such that the absolute value |E_n| is prime (the absolute value is needed since E_n takes on alternating positive and negative ...

The four parameters e_0, e_1, e_2, and e_3 describing a finite rotation about an arbitrary axis. The Euler parameters are defined by e_0 = cos(phi/2) (1) e = [e_1; e_2; e_3] ...

The Euler points are the midpoints E_A, E_B, E_C of the segments which join the vertices A, B, and C of a triangle DeltaABC and the orthocenter H. They are three of the nine ...

Let a prime number generated by Euler's prime-generating polynomial n^2+n+41 be known as an Euler prime. (Note that such primes are distinct from prime Euler numbers, which ...

A square array made by combining n objects of two types such that the first and second elements form Latin squares. Euler squares are also known as Graeco-Latin squares, ...

A mathematical structure first introduced by Kolyvagin (1990) and defined as follows. Let T be a finite-dimensional p-adic representation of the Galois group of a number ...

Let O and I be the circumcenter and incenter of a triangle with circumradius R and inradius r. Let d be the distance between O and I. Then d^2=R(R-2r) (Mackay 1886-1887; ...

An Eulerian path, also called an Euler chain, Euler trail, Euler walk, or "Eulerian" version of any of these variants, is a walk on the graph edges of a graph which uses each ...

Euler's continued fraction is the name given by Borwein et al. (2004, p. 30) to Euler's formula for the inverse tangent, ...