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Re: "Complement" to the Risch Algorithm

  • To: mathgroup at smc.vnet.net
  • Subject: [mg131459] Re: "Complement" to the Risch Algorithm
  • From: Richard Fateman <fateman at cs.berkeley.edu>
  • Date: Sat, 27 Jul 2013 05:38:54 -0400 (EDT)
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  • References: <ksq0os$8na$1@smc.vnet.net>

On 7/24/13 6:58 PM, Matthias Bode wrote:
> Hola:
>
> Motivated by An analytical solution to an integral not currently in Mathematica? and by the interview with Mr. Daniel Lichtblau

on omega tau
Huh?  oh, I found it using Google.

three questions arose to me:
>
> 1. Are there theorems that prove that particular types of functions - e. g.  x^(1/x) - can not be integrated?
Yes. You can find "integration in finite terms" discussions (including 
by Risch, and successors e.g. Bronstein) via Google.
>
>
> Or:
>
>
> 2. Is there a theorem which proves that theorems as per 1. above can not exist?
No, see above.
>
>
> Or:
>
>
> 3. Is this an undecidable problem?
Since you cannot tell in general if a factor of an integrand is zero or 
not, you cannot tell if you can integrate or not.

Suggestion:  Google for  {undecidable integration}

Important hint for effective use of the internet. Instead of posting a 
question or 3 here first, try to use the Google. It is your friend.
RJF

>



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