Hermite polynomials given above. Physicist Scaling Convention The generalized Laguerre polynomials are used to describe the quantum wavefunction for hydrogen atom orbitals. In the introductory literature on this topic, a different scaling is used for the generalized Laguerre polynomials than the scaling presented in this article. In the convention taken here, the generalized Laguerre polynomials can be expressed as where is the confluent hypergeometric function. In the physicist literature, such as , the generalized Laguerre polynomials are instead defined as The physicist version is related to the standard version by There is yet another convention in use, though less frequently, in the physics literature. Under this convention the Laguerre polynomials are given by See also Orthogonal polynomials Rodrigues' formula Angelescu polynomials Bessel polynomials Denisyuk polynomials Transverse mode, an important application of Laguerre polynomials to describe the field intensity within a waveguide or laser beam profile. Notes References G. Szegő, Orthogonal polynomials, 4th edition, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, RI, 1975. B. Spain, M.G. Smith, Functions of mathematical physics, Van Nostrand Reinhold Company, London, 1970. Chapter 10 deals with Laguerre polynomials. Eric W. Weisstein, "Laguerre Polynomial", From MathWorld—A Wolfram Web Resource. External links Polynomials Orthogonal polynomials Special hypergeometric functions