[I think this didn't reach the list yesterday due to a server problem in
Zurich. Apologies if it is a duplicate.]
On 10 Apr 2015, at 05:39 , Harris A. Jaffee <h...@jhu.edu> wrote:
> I agree, and the text is less than ideal in several other places.
> But I don't especially like your phrase 'infinite range', even
> though the idea is right. I think the necessary terminology
> already exists. How about something like this?
>
> There are interfaces (defined in header R_ext/Applic.h) for definite
> ("proper") and for _improper_ integrals, improper meaning that at
> least one of the limits of integration is infinite.
Nope. Improper integrals are a subset of definite integrals. E.g., the very
first explicit integral in Mathematical Handbook's section on definite
integrals, under the heading "Definite integrals involving rational or
irrational expressions" is \int_0^\infty dx/(x^2+a^2) = \pi/2a. Also, an
integral can be improper even when it is over a finite interval if there is an
internal singularity.
But the whole thing depends on which version of integration theory you adopt.
Lebesgue integration doesn't really bother with distinguishing between finite
and infinite ranges of integration and proper/improper, it just has some
functions where the integral is undefined.
For the purposes of "Writing R Extensions", I'd say that "integrals over finite
and infinite intervals" should do fine. A fair amount of the complexity of
numerical integration has to be glossed over anyway. The existing text is
clearly wrong, of course.
-pd
>
> Moving ahead, I would use Definite and Improper for "Finite:" and
> "Indefinite:".
>
>> On Apr 9, 2015, at 7:13 PM, William Dunlap <wdun...@tibco.com> wrote:
>>
>> In 'Writing R Extensions' section 6.9 there is the paragraph
>>
>> There are interfaces (defined in header R_ext/Applic.h) for definite and
>> for indefinite integrals. ‘Indefinite’ means that at least one of the
>> integration boundaries is not finite.
>>
>> An indefinite integral usually means an antiderivative, not an integral
>> over an infinite spread. Should that first sentence end with 'for
>> integrals over finite and infinite ranges' and the second sentence omitted?
>>
>> Bill Dunlap
>> TIBCO Software
>> wdunlap tibco.com
>>
>> [[alternative HTML version deleted]]
>>
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--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
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Email: pd....@cbs.dk Priv: pda...@gmail.com
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