Search Results for ""

There are a great many beautiful identities involving q-series, some of which follow directly by taking the q-analog of standard combinatorial identities, e.g., the ...

The Jacobi elliptic functions are standard forms of elliptic functions. The three basic functions are denoted cn(u,k), dn(u,k), and sn(u,k), where k is known as the elliptic ...

Cubic symmetric graphs are sometimes called Foster graphs and denoted F_(nnn)X, where nnn is the vertex count and X is a letter A, B, C, ... indicating the particular such ...

Synthetic division is a shortcut method for dividing two polynomials which can be used in place of the standard long division algorithm. This method reduces the dividend and ...

A perfect magic cube is a magic cube for which the rows, columns, pillars, space diagonals, and diagonals of each n×n orthogonal slice sum to the same number (i.e., the magic ...

A graph is planar if it can be drawn in a plane without graph edges crossing (i.e., it has graph crossing number 0). The number of planar graphs with n=1, 2, ... nodes are 1, ...

The xi-function is the function xi(z) = 1/2z(z-1)(Gamma(1/2z))/(pi^(z/2))zeta(z) (1) = ((z-1)Gamma(1/2z+1)zeta(z))/(sqrt(pi^z)), (2) where zeta(z) is the Riemann zeta ...

A sphere with two handles and two holes, i.e., a genus-2 torus.

The inversion of a horn torus. If the inversion center lies on the torus, then the horn cyclide degenerates to a parabolic horn cyclide.

A parabolic cyclide formed by inversion of a horn torus when the inversion sphere is tangent to the torus.