LaguerreL[n, x]
gives the Laguerre polynomial .

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 .
  • They satisfy the differential equation .
  • For certain special arguments, LaguerreL automatically evaluates to exact values.
  • LaguerreL can be evaluated to arbitrary numerical precision.
  • LaguerreL automatically threads over lists.
  • LaguerreL[n, x] is an entire function of x with no branch cut discontinuities.
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