Integrate Bug...
- To: mathgroup at yoda.physics.unc.edu
- Subject: Integrate Bug...
- From: anna
- Date: Tue, 30 Nov 93 14:36:19 CST
Following integral has not been fixed in V2.2, and we still have
that bug:
In[1]:= Integrate[ u^(5/6) (1 - u)^(5/6) Cos[k u], {u,0,1}]
On::none: Message SeriesData::csa not found.
General::intinit: Loading integration packages -- please wait.
2 2
2 1/3 4 Sqrt[k ] Sqrt[k ] 11
(k ) Sqrt[Pi] BesselJ[-, --------] Cos[--------] Gamma[--]
3 2 2 6
Out[1]= -------------------------------------------------------------
1/3 2
2 2 k
In new V2.3 this bug has been fixed.
In[272]:= Integrate[ u^(5/6) (1 - u)^(5/6) Cos[k u], {u,0,1}]
11 4 k Sign[k] k
Sqrt[Pi] Gamma[--] BesselJ[-, ---------] Cos[-]
6 3 2 2
Out[272]= If[Im[k] == 0, -----------------------------------------------,
2 2/3
(k )
5/6 5/6
> Integrate[(1 - u) u Cos[k u], {u, 0, 1}]]
Now this result is right for all real and integer K
The result from Prudnikov, Brychkov, and Marichev
res = k^(-4/3) Sqrt[Pi] BesselJ[4/3, k/2] Cos[k/2] Gamma[11/6];
In[277]:= N[res/. k -> -1/4]
-16
Out[277]= 0.218449 - 1.63992 10 I
In[278]:= N[%272/. k -> -1/4]
Out[278]= 0.218449
In[279]:= u^(5/6) (1 - u)^(5/6) Cos[k u]/. k -> -1/4;
In[280]:= NIntegrate[%, {u, 0, 1}]
Out[280]= 0.218449
Anna Marichev