DOCUMENTATION CENTER SEARCH
Mathematica
>
Special Functions
>
Built-in
Mathematica
Symbol
Orthogonal Polynomials
Tutorials »
|
HermiteH
WhittakerM
WhittakerW
Hypergeometric1F1
See Also »
|
Functions for Separable Coordinate Systems
Functions Used in Quantum Mechanics
Mathematical Functions
Special Functions
More About »
LaguerreL
LaguerreL
[
n
,
x
]
gives the Laguerre polynomial
.
LaguerreL
[
n
,
a
,
x
]
gives the generalized Laguerre polynomial
.
MORE INFORMATION
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
CLOSE ALL
Basic Examples
(3)
Compute the 5
LaguerreL
:
In[1]:=
Out[1]=
Plot the 10
Laguerre polynomial:
In[1]:=
Out[1]=
Compute the associated Laguerre polynomial
:
In[1]:=
Out[1]=
Scope
(6)
Generalizations & Extensions
(1)
Applications
(3)
Properties & Relations
(2)
Possible Issues
(1)
SEE ALSO
HermiteH
WhittakerM
WhittakerW
Hypergeometric1F1
TUTORIALS
Orthogonal Polynomials
RELATED LINKS
MathWorld
The Wolfram Functions Site
NKS|Online
(
A New Kind of Science
)
MORE ABOUT
Functions for Separable Coordinate Systems
Functions Used in Quantum Mechanics
Mathematical Functions
Special Functions
New in 1
© 2008 Wolfram Research, Inc.
. 
. 
.
EXAMPLES
Basic Examples 
Scope 