This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

LaguerreL

LaguerreL[n, x]
gives the Laguerre polynomial L_n(x).
LaguerreL[n, a, x]
gives the generalized Laguerre polynomial .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • Explicit polynomials are given when possible.
  • .
  • The Laguerre polynomials are orthogonal with weight function x^ae^(-x).
  • They satisfy the differential equation x​y^(′′)+(a+1-x)​y^′+n​y=0.
  • For certain special arguments, LaguerreL automatically evaluates to exact values.
  • LaguerreL can be evaluated to arbitrary numerical precision.
  • LaguerreL[n, x] is an entire function of x with no branch cut discontinuities.
New in 1