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The spherical Bessel function of the first kind, denoted j_nu(z), is defined by j_nu(z)=sqrt(pi/(2z))J_(nu+1/2)(z), (1) where J_nu(z) is a Bessel function of the first kind ...

A map projection obtained by projecting points P on the surface of sphere from the sphere's north pole N to point P^' in a plane tangent to the south pole S (Coxeter 1969, p. ...

Rather surprisingly, trigonometric functions of npi/17 for n an integer can be expressed in terms of sums, products, and finite root extractions because 17 is a Fermat prime. ...

The Whittaker functions arise as solutions to the Whittaker differential equation. The linearly independent solutions to this equation are M_(k,m)(z) = ...

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 ...

A modified set of Chebyshev polynomials defined by a slightly different generating function. They arise in the development of four-dimensional spherical harmonics in angular ...

The cosine function cosx is one of the basic functions encountered in trigonometry (the others being the cosecant, cotangent, secant, sine, and tangent). Let theta be an ...

The figure eight knot, also known as the Flemish knot and savoy knot, is the unique prime knot of four crossings 04-001. It has braid word ...

Seeks to obtain the best numerical estimate of an integral by picking optimal abscissas x_i at which to evaluate the function f(x). The fundamental theorem of Gaussian ...

Numerical integration is the approximate computation of an integral using numerical techniques. The numerical computation of an integral is sometimes called quadrature. ...