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The Alexander invariant H_*(X^~) of a knot K is the homology of the infinite cyclic cover of the complement of K, considered as a module over Lambda, the ring of integral ...

The term "Aristotle gap"' is introduced in this work to refer to the angle between the first and last member of a 5-tetrahedral ring. This gap has angle measure theta = ...

The integral int_0^1x^p(1-x)^qdx, called the Eulerian integral of the first kind by Legendre and Whittaker and Watson (1990). The solution is the beta function B(p+1,q+1).

The term Bol loop refers to either of two classes of algebraic loops satisfying the so-called Bol identities. In particular, a left Bol loop is an algebraic loop L which, for ...

The Brent-Salamin formula, also called the Gauss-Salamin formula or Salamin formula, is a formula that uses the arithmetic-geometric mean to compute pi. It has quadratic ...

Consider a broadcast scheme on a connected graph from an originator vertex v in a graph G consisting of a sequence of parallel calls starting from v. In each time step, every ...

The cyclic group C_(10) is the unique Abelian group of group order 10 (the other order-10 group being the non-Abelian D_5). Examples include the integers modulo 10 under ...

The Dirichlet lambda function lambda(x) is the Dirichlet L-series defined by lambda(x) = sum_(n=0)^(infty)1/((2n+1)^x) (1) = (1-2^(-x))zeta(x), (2) where zeta(x) is the ...

The third singular value k_3, corresponding to K^'(k_3)=sqrt(3)K(k_3), (1) is given by k_3=sin(pi/(12))=1/4(sqrt(6)-sqrt(2)). (2) As shown by Legendre, ...

The term "Euler function" may be used to refer to any of several functions in number theory and the theory of special functions, including 1. the totient function phi(n), ...