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DOCUMENTATION CENTER SEARCH
Mathematica
>
Mathematics and Algorithms
>
Mathematical Functions
>
Special Functions
>
Built-in
Mathematica
Symbol
Orthogonal Polynomials
Tutorials »
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ChebyshevT
GegenbauerC
JacobiP
See Also »
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Special Functions
More About »
ChebyshevU
ChebyshevU
[
n
,
x
]
gives the Chebyshev polynomial of the second kind
.
MORE INFORMATION
Mathematical function, suitable for both symbolic and numerical manipulation.
Explicit polynomials are given for integer
n
.
.
For certain special arguments,
ChebyshevU
automatically evaluates to exact values.
ChebyshevU
can be evaluated to arbitrary numerical precision.
ChebyshevU
automatically threads over lists.
ChebyshevU
[
n
,
z
]
has a branch cut discontinuity in the complex
z
plane running from
-
to
for noninteger
n
.
EXAMPLES
CLOSE ALL
Basic Examples
(2)
Compute the
ChebyshevU
polynomial:
In[1]:=
Out[1]=
In[1]:=
Out[1]=
Scope
(6)
Generalizations & Extensions
(2)
Applications
(3)
Properties & Relations
(3)
Possible Issues
(1)
SEE ALSO
ChebyshevT
GegenbauerC
JacobiP
TUTORIALS
Orthogonal Polynomials
RELATED LINKS
Demonstrations with ChebyshevU
(
Wolfram Demonstrations Project
)
MathWorld
The Wolfram Functions Site
MORE ABOUT
Special Functions
New in 1
. ![U_n(cos theta)=sin[(n+1)theta]/sin theta](Files/ChebyshevU.en/2.gif "U_n(cos theta)=sin[(n+1)theta]/sin theta"){kind=small}
. 
to 
for noninteger n.
EXAMPLES
Basic Examples 
Scope 