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Re: Some bugs in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg59253] Re: Some bugs in Mathematica
• From: akhmel at hotmail.com
• Date: Wed, 3 Aug 2005 01:19:56 -0400 (EDT)
• References: <200508010505.BAA24522@smc.vnet.net><dcmv3n$gqa$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

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?

• Follow-Ups:
  • Re: Re: Some bugs in Mathematica
    • From: Selwyn Hollis <sh2.7183@earthlink.net>

• References:
  • Some bugs in Mathematica
    • From: akhmel@hotmail.com