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