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The inversive distance is the natural logarithm of the ratio of two concentric circles into which the given circles can be inverted. Let c be the distance between the centers ...

The function f_theta(z)=z/((1+e^(itheta)z)^2) (1) defined on the unit disk |z|<1. For theta in [0,2pi), the Köbe function is a schlicht function f(z)=z+sum_(j=2)^inftya_jz^j ...

König's line coloring theorem states that the edge chromatic number of any bipartite graph equals its maximum vertex degree. In other words, every bipartite graph is a class ...

The Lommel differential equation is a generalization of the Bessel differential equation given by z^2y^('')+zy^'+(z^2-nu^2)y=kz^(mu+1), (1) or, in the most general form, by ...

The Lucas polynomials are the w-polynomials obtained by setting p(x)=x and q(x)=1 in the Lucas polynomial sequence. It is given explicitly by ...

The "mathematical paradigm" is a term that may be applied to the fundamental idea that events in the world can be described by mathematical equations, and that solutions to ...

Let f(x) be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then there is at least one point c in (a,b) such that ...

Let G=(V,E) be a (not necessarily simple) undirected edge-weighted graph with nonnegative weights. A cut C of G is any nontrivial subset of V, and the weight of the cut is ...

Murata's constant is defined as C_(Murata) = product_(p)[1+1/((p-1)^2)] (1) = 2.82641999... (2) (OEIS A065485), where the product is over the primes p. It can also be written ...

Curves with Cartesian equation ay^2=x(x^2-2bx+c) with a>0. The above equation represents the third class of Newton's classification of cubic curves, which Newton divided into ...