LaguerreL

LaguerreL[n,x]

gives the Laguerre polynomial .

LaguerreL[n,a,x]

gives the generalized Laguerre polynomial .

Details

  • 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.

Examples

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Basic Examples  (3)

Compute the 5^(th) LaguerreL:

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Plot the 10^(th) Laguerre polynomial:

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Compute the associated Laguerre polynomial :

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Scope  (6)

Generalizations & Extensions  (1)

Applications  (4)

Properties & Relations  (7)

Possible Issues  (1)

See Also

HermiteH  WhittakerM  WhittakerW  Hypergeometric1F1

Tutorials

Introduced in 1988
(1.0)