Integrate Bug...
- To: mathgroup at yoda.physics.unc.edu
- Subject: Integrate Bug...
- From: zollars at ll.mit.edu (Byron Zollars)
- Date: Fri, 19 Nov 93 15:30:56 -0500
- Cc: zollars at ll.mit.edu
- Reply-to: zollars at ll.mit.edu
I was dismayed to find that Mathematica gave me the wrong answer to this integral:
--------------------
Mathematica 2.2 for Macintosh
Copyright 1988-93 Wolfram Research, Inc.
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
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The correct answer, obtained with either manual manipulation using the Mellin
convolution theorem, or the wonderful text of Prudnikov, Brychkov, and Marichev
gives the correct result of:
k^(-4/3) Sqrt[Pi] BesselJ[4/3, k/2] Cos[k/2] Gamma[11/6],
which is different than the Mma result by the factor of 2^(4/3).
Is this an isolated bug, or have others out there found similar problems??
Is there a fix for this bug?
-----------------------------------------
| Byron Zollars <zollars at ll.mit.edu> |
| Laser and Sensor Applications Group |
| MIT / Lincoln Laboratory |
| 244 Wood St. HW45-375 |
| Lexington, MA 02173 (617)981-3604 |
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