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SEARCH MATHEMATICA 8 DOCUMENTATION
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE
DOCUMENTATION CENTER
FOR THE LATEST INFORMATION.
Mathematica
>
Special Functions
>
Built-in
Mathematica
Symbol
Orthogonal Polynomials
Tutorials »
|
LegendreP
ClebschGordan
SphericalBesselJ
ZernikeR
See Also »
|
Functions for Separable Coordinate Systems
Functions Used in Optics
Functions Used in Quantum Mechanics
Special Functions
More About »
SphericalHarmonicY
SphericalHarmonicY
[
l
,
m
,
,
]
gives the spherical harmonic
.
MORE INFORMATION
Mathematical function, suitable for both symbolic and numerical manipulation.
The spherical harmonics are orthonormal with respect to integration over the surface of the unit sphere.
For
,
where
is the associated Legendre function.
For
,
.
For certain special arguments,
SphericalHarmonicY
automatically evaluates to exact values.
SphericalHarmonicY
can be evaluated to arbitrary numerical precision.
SphericalHarmonicY
automatically threads over lists.
EXAMPLES
CLOSE ALL
Basic Examples
(1)
In[1]:=
Out[1]=
Scope
(5)
Generalizations & Extensions
(1)
Applications
(1)
Properties & Relations
(1)
SEE ALSO
LegendreP
ClebschGordan
SphericalBesselJ
ZernikeR
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 Optics
Functions Used in Quantum Mechanics
Special Functions
New in 1
© 2013 Wolfram Research, Inc.
, 
]
. 
, 
where 
is the associated Legendre function. 
, 
.
EXAMPLES
Basic Examples 
Scope 