Re: Re: Some bugs in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg59282] Re: [mg59253] Re: Some bugs in Mathematica
- From: Selwyn Hollis <sh2.7183 at earthlink.net>
- Date: Thu, 4 Aug 2005 02:08:05 -0400 (EDT)
- References: <200508010505.BAA24522@smc.vnet.net><dcmv3n$gqa$1@smc.vnet.net> <200508030519.BAA06378@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
On Aug 3, 2005, at 1:19 AM, akhmel at hotmail.com wrote:
>
> Zhengji Li wrote:
>
>> For No.1, I think the result should be (n - 1) Pi / 2, where n >= 1.
>> You can use this to verify it:
>>
>> Table[Sum[(Gamma[n - k - 1/2]*Gamma[k + 1/2])/(Gamma[n - k -
>> 1]*Gamma[k + 1]), {k, 0, n - 1 + 4}], {n, 1, 10}]
>>
>> For No. 2, the result is just correct. You can use D[.., r] to verify
>> it. You can see the help of AppellF1, there is a more generalized
>> version of your integral.
>>
>> For No. 3, I wonder why you want to do the integral over [x, b].
>> There
>> are several singular values in the function, and the result will
>> differ under different conditions. I think Mathematica's "result" is
>> reasonable, since it maybe too complicated for it to judge how to do
>> this leak-of-constraint integral.
>>
>
> 1) Why did you write the summation limit as k= 0 to n-1+4? The correct
> upper limit is n-1. With this upper limit and n>=1, the correct result
> is 1 and Mathematica doesn't use it.
> 2) I didn't say that Mathematica gives incorrect results, I said that
> Appel function is an over complication, because the simplest result is
> a logarithm.
> 3) It's irrelevant why I want to compute the integral I want to
> compute. What is relevant is that Mathematica is unable to compute a
> very elementary integral and this is a shame.
>
> Is everything clear?
>
>
Re (1): Mathematica 5.2 does not return the incorrect 0 result.
Versions 5.0 and 5.1 do.
Re (2): After doing a little digging, I can't find any reference to
how an Appell F1 ever reduces to a logarithm. I'm curious as to what
exactly is the answer you wish to obtain.
Re (3): Again, what elementary result are you expecting?
Selwyn Hollis
- References:
- Some bugs in Mathematica
- From: akhmel@hotmail.com
- Re: Some bugs in Mathematica
- From: akhmel@hotmail.com
- Some bugs in Mathematica