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In mathematics, a formula is a fact, rule, or principle that is expressed in terms of mathematical symbols. Examples of formulas include equations, equalities, identities, ...

Let (x_1,x_2) and (y_1,y_2) be two sets of complex numbers linearly independent over the rationals. Then the four exponential conjecture posits that at least one of ...

Let n>=0 and alpha_1, alpha_2, ...be the positive roots of J_n(x)=0, where J_n(z) is a Bessel function of the first kind. An expansion of a function in the interval (0,1) in ...

The Fourier cosine transform of a real function is the real part of the full complex Fourier transform, F_x^((c))[f(x)](k) = R[F_x[f(x)](k)] (1) = ...

The frame bundle on a Riemannian manifold M is a principal bundle. Over every point p in M, the Riemannian metric determines the set of orthonormal frames, i.e., the possible ...

The generalized diameter is the greatest distance between any two points on the boundary of a closed figure. The diameter of a subset E of a Euclidean space R^n is therefore ...

Geometry is the study of figures in a space of a given number of dimensions and of a given type. The most common types of geometry are plane geometry (dealing with objects ...

A Goldbach number is a positive integer that is the sum of two odd primes (Li 1999). Let E(x) (the "exceptional set of Goldbach numbers") denote the number of even numbers ...

Let (a)_i be a sequence of complex numbers and let the lower triangular matrices F=(f)_(nk) and G=(g)_(nk) be defined as f_(nk)=(product_(j=k)^(n-1)(a_j+k))/((n-k)!) and ...

The kth power of a graph G is a graph with the same set of vertices as G and an edge between two vertices iff there is a path of length at most k between them (Skiena 1990, ...