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There exist a variety of formulas for either producing the nth prime as a function of n or taking on only prime values. However, all such formulas require either extremely ...

A quadratic equation is a second-order polynomial equation in a single variable x ax^2+bx+c=0, (1) with a!=0. Because it is a second-order polynomial equation, the ...

For |q|<1, the Rogers-Ramanujan identities are given by (Hardy 1999, pp. 13 and 90), sum_(n=0)^(infty)(q^(n^2))/((q)_n) = 1/(product_(n=1)^(infty)(1-q^(5n-4))(1-q^(5n-1))) ...

The sine function sinx is one of the basic functions encountered in trigonometry (the others being the cosecant, cosine, cotangent, secant, and tangent). Let theta be an ...

An additive cellular automaton is a cellular automaton whose rule is compatible with an addition of states. Typically, this addition is derived from modular arithmetic. ...

A branch cut is a curve (with ends possibly open, closed, or half-open) in the complex plane across which an analytic multivalued function is discontinuous. For convenience, ...

There are four strongly regular graphs with parameters (nu,k,lambda,mu)=(28,12,6,4), one of them being the triangular graph of order 8. The other three such graphs are known ...

Christoffel symbols of the second kind are the second type of tensor-like object derived from a Riemannian metric g which is used to study the geometry of the metric. ...

The conjugate gradient method is an algorithm for finding the nearest local minimum of a function of n variables which presupposes that the gradient of the function can be ...

A convex polyomino (sometimes called a "convex polygon") is a polyomino whose perimeter is equal to that of its minimal bounding box (Bousquet-Mélou et al. 1999). ...