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MathGroup Archive 2007

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Re: Re: strange behavior of Integrate


dimitris wrote:
>>[...]
I had asked:
>>Why is this integral important?


The reply:

>>>int = HoldForm[(1/Pi)*Integrate[Log[x/(x^2 + 1)]*(1/(x^2 + 1)^m), {x,=
> 
> 0, Infinity}, Assumptions -> m >= 1]]
> 
> I study the book "Irresistible Integrals" by George Boros and Victor
> Moll
> (2nd Edition, Campridge University Press 2006).
> I work various formulas by hand and Mathematica from this book and one
> of worked examples is this integral (page 270).
> 
> (BTW, very good performance of Mathematica)
> 
> Is is a good reason or not?
> 
> Best Regards
> Dimitris

It's a solid book and, hence, a sound reason. But only when stated 
explicitly. Problems that appear out of nowhere, so to speak, are likely 
to be taken less seriously. Integrals that appear in various books such 
as that of Boros and Moll come with a pedigree of sorts. That at least 
is my opinion (biased in part because they develop some methods 
involving what I find to be interesting mathematics).

Needless to say, integrals, exact or numeric, that appear in the course 
of one's research are also quite important (especially to the 
researcher). In determining priority levels for purposes of triage, this 
question of origin is one thing I tend to take into account. Examples 
that exist merely to illustrate pathology are regarded as iteresting, 
but not, in general, as high priority bugs.

Victor Moll also sometimes sends such examples.


Daniel Lichtblau
Wolfram Research






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