       Re: "At long last, Sir, have you no shame?"

• To: mathgroup at smc.vnet.net
• Subject: [mg18524] Re: "At long last, Sir, have you no shame?"
• From: colin at tri.org.au (Colin Rose)
• Date: Thu, 8 Jul 1999 22:32:57 -0400
• Organization: Theoretical Research Institute
• References: <7luk6s\$l95@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```David Withoff <withoff at wolfram.com> wrote:

> independent experts often disagree about what is or is not a bug.

Two cases instantly come to mind:

1.   Sum in v4
_________

Consider say:

In:=     g = Exp[-i];

In:=     Sum[g, {i, 1, n}]

Out=     n/E^i

which is nonsense. This happens for almost ANY expression g=g(i).
To get the correct answer, you have to wrap Evaluate around g:

In:=      Sum[Evaluate[g], {i, 1, n}]
Out=      (-1 + E^n)/(E^n*(-1 + E))

Wolfram support says Out is not a bug, since Sum has attribute HoldAll.
I say it is clearly (and obviously) an extremely serious bug,
in the sense that it gives the wrong answer to almost any Summation
where g is pre-defined. I reported  it under v4 alpha, it was fixed
in the betas, and it is now back in the v4 final release. But then
it isn't a bug, apparently !?

2.  Non-convergent integrals
________________________

Or how about the mean of a Cauchy random variable:

In:=   f = 1/(Pi(1 + x^2));

In:=   Integrate[x*f, {x, -Infinity, Infinity},
GenerateConditions -> False]
Out=   I

The correct answer is that the integral does not converge.
WRI claims it is not a bug, and won't fix it, even though:
(i) GenerateConditions -> True yields the
correct answer (convergence error), and
(ii) there are no conditions stated here anyway, so it is
not apparent why GenerateConditions -> False should yield a
different solution to -> True.

This is actually a general problem, with similar behaviour
in the Levy family,
f = (1/Sqrt[2*Pi]*Exp[-(1/(2*y))])/y^(3/2);
where the moments do not exist either.

___________

Cheers

Colin

--
Colin Rose
tr(I)    -  Theoretical Research Institute
__________________________________________
colin at tri.org.au    http://www.tri.org.au/

```

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