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The modular equation of degree five can be written (u/v)^3+(v/u)^3=2(u^2v^2-1/(u^2v^2)).

There are four varieties of Airy functions: Ai(z), Bi(z), Gi(z), and Hi(z). Of these, Ai(z) and Bi(z) are by far the most common, with Gi(z) and Hi(z) being encountered much ...

Solutions to the associated Laguerre differential equation with nu!=0 and k an integer are called associated Laguerre polynomials L_n^k(x) (Arfken 1985, p. 726) or, in older ...

The beta function B(p,q) is the name used by Legendre and Whittaker and Watson (1990) for the beta integral (also called the Eulerian integral of the first kind). It is ...

The Boy surface is a nonorientable surface that is one possible parametrization of the surface obtained by sewing a Möbius strip to the edge of a disk. Two other ...

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. ...

For every positive integer n, there exists a circle which contains exactly n lattice points in its interior. H. Steinhaus proved that for every positive integer n, there ...

The self-intersection of a one-sided surface. The word "cross-cap" is sometimes also written without the hyphen as the single word "crosscap." The cross-cap can be thought of ...

A n-crossed prism graph for positive even n (a term introduced here for the first time), is a graph obtained by taking two disjoint cycle graphs C_n and adding edges ...

Dawson's integral (Abramowitz and Stegun 1972, pp. 295 and 319), also sometimes called Dawson's function, is the entire function given by the integral F(x) = ...