GegenbauerC
Usage
Notes
Further Examples
Here are the first ten GegenbauerC polynomials for .
In[1]:=
|
Out[1]//TableForm=
|
The Gegenbauer polynomials are pairwise orthogonal with respect to the appropriate weight function.
In[2]:=
|
Out[2]=
|
This is the derivative.
In[3]:=
|
Out[3]=
|
This is the indefinite integral.
In[4]:=
|
Out[4]=
|
This verifies the defining differential equation for and .
In[5]:=
|
In[6]:=
|
Out[6]=
|
This is the series expansion around to order .
In[7]:=
|
Out[7]=
|
Here FunctionExpand expresses a special case of GegenbauerC in terms of more fundamental functions.
In[8]:=
|
Out[8]=
|
In[9]:=
|
|