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The hyperbolic functions sinhz, coshz, tanhz, cschz, sechz, cothz (hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cosecant, hyperbolic secant, and ...

A point lattice is a regularly spaced array of points. In the plane, point lattices can be constructed having unit cells in the shape of a square, rectangle, hexagon, etc. ...

Separation of variables is a method of solving ordinary and partial differential equations. For an ordinary differential equation (dy)/(dx)=g(x)f(y), (1) where f(y)is nonzero ...

A k-matching in a graph G is a set of k edges, no two of which have a vertex in common (i.e., an independent edge set of size k). Let Phi_k be the number of k-matchings in ...

pi has decimal expansion given by pi=3.141592653589793238462643383279502884197... (1) (OEIS A000796). The following table summarizes some record computations of the digits of ...

The associated Legendre polynomials P_l^m(x) and P_l^(-m)(x) generalize the Legendre polynomials P_l(x) and are solutions to the associated Legendre differential equation, ...

The Legendre polynomials, sometimes called Legendre functions of the first kind, Legendre coefficients, or zonal harmonics (Whittaker and Watson 1990, p. 302), are solutions ...

Let N steps of equal length be taken along a line. Let p be the probability of taking a step to the right, q the probability of taking a step to the left, n_1 the number of ...

The spherical harmonics Y_l^m(theta,phi) are the angular portion of the solution to Laplace's equation in spherical coordinates where azimuthal symmetry is not present. Some ...

The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, ...