Laguerre polynomials

In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are solutions of Laguerre's equation: In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are solutions of Laguerre's equation: which is a second-order linear differential equation. This equation has nonsingular solutions only if n is a non-negative integer. Sometimes the name Laguerre polynomials is used for solutions of where n is still a non-negative integer.Then they are also named generalized Laguerre polynomials, as will be done here (alternatively associated Laguerre polynomials or, rarely, Sonine polynomials, after their inventor Nikolay Yakovlevich Sonin). More generally, a Laguerre function is a solution when n is not necessarily a non-negative integer. The Laguerre polynomials are also used for Gaussian quadrature to numerically compute integrals of the form These polynomials, usually denoted L0, L1, ..., are a polynomial sequence which may be defined by the Rodrigues formula,