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Re: Re: A Problem with Simplify

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87647] Re: [mg87603] Re: A Problem with Simplify
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Tue, 15 Apr 2008 05:48:31 -0400 (EDT)
  • References: <ftkb7f$a9m$1@smc.vnet.net> <200804140943.FAA08090@smc.vnet.net>

Alexey Popkov wrote:
> On Apr 10, 10:14 am, "Kevin J. McCann" <Kevin.McC... at umbc.edu> wrote:
> 
>>I have the following rather simple integral of two sines, which should
>>evaluate to zero if m is not equal to n and to L/2 if they are the same.
> 
> 
> Try the following:
> Integrate[Exp[(a - 1)*x], x] /. a -> 1
> Integrate[Cos[(a - 1)*x], x] /. a -> 1
> Integrate[(a - 1)^x, {x, -1, 0}] /. a -> 1
> Integrate[Cos[a x]/Sin[x], x] /. a -> 1
> 
> There is the ONE underlying BUG! In some complicated cases this bug
> may result in random partial answers.
> 
> http://forum.ru-board.com/topic.cgi?forum=5&topic=10291&start=80#9

Removing the replacements, here are the Integrate results.

In[17]:= InputForm[Integrate[Exp[(a - 1)*x], x]]
Out[17]//InputForm= E^((-1 + a)*x)/(-1 + a)

In[18]:= InputForm[Integrate[Cos[(a - 1)*x], x]]
Out[18]//InputForm= Sin[(-1 + a)*x]/(-1 + a)

In[19]:= InputForm[Integrate[(a - 1)^x, {x, -1, 0}]]
Out[19]//InputForm= (-2 + a)/((-1 + a)*Log[-1 + a])

In[20]:= InputForm[Integrate[Cos[a*x]/Sin[x], x]]
Out[20]//InputForm=
((1 + a)*Hypergeometric2F1[1/2 - a/2, 1, 3/2 - a/2, E^((2*I)*x)] -
   (-1 + a)*E^((2*I)*a*x)*Hypergeometric2F1[(1 + a)/2, 1, (3 + a)/2,
     E^((2*I)*x)])/((-1 + a^2)*E^(I*(-1 + a)*x))

As far as I am aware thse are correct. What is the bug?

Daniel Lichtblau
Wolfram Research





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