Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1993
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1993

[Date Index] [Thread Index] [Author Index]

Search the Archive

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

-----------------------
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   |
-----------------------------------------





  • Prev by Date: Re: Naming the Mathematica language
  • Next by Date: Mathematica Symbolic Toolbox for MATLAB
  • Previous by thread: Name for new language
  • Next by thread: Integrate Bug...