BUILT-IN MATHEMATICA SYMBOL

# LaguerreL

LaguerreL[n, x]
gives the Laguerre polynomial .

LaguerreL[n, a, x]
gives the generalized Laguerre polynomial .

## DetailsDetails

• 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.

## ExamplesExamplesopen allclose all

### Basic Examples (3)Basic Examples (3)

Compute the 5 LaguerreL:

 Out[1]=

Plot the 10 Laguerre polynomial:

 Out[1]=

Compute the associated Laguerre polynomial :

 Out[1]=

## TutorialsTutorials

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