[106] in mathematical software users group
Re: Standard integrals in Maple
daemon@ATHENA.MIT.EDU (Reid M. Pinchback)
Fri Aug 13 16:49:10 1993
To: mbgordy@Athena.MIT.EDU
Cc: msug@MIT.EDU
Date: Fri, 13 Aug 93 16:46:50 EDT
From: "Reid M. Pinchback" <reidmp@Athena.MIT.EDU>
Ok, this should solve the problem. Luckily I saved some old email
with the solution sent to me by Mike Monagan.
In article <1qjpj5INN6hq@senator-bedfellow.MIT.EDU>, reidmp@athena.mit.edu (Reid M. Pinchback) writes:
> In article <1993Apr14.192258.10688@news.uiowa.edu>, haferman@icaen.uiowa.edu (Jeff Haferman) writes:
> >in terms of the gamma function, i.e., is there anyway
> >to get Maple to evaluate
> > int( exp(-t)*t^(z-1), t=0..infinity );
> >so that it returns
> > GAMMA(z)?
>
> From what I can see, even in release 2, the answer is no. The
> 'mellin' transform function knows about 'GAMMA', but 'int' doesn't
> seem to. Maybe you should seen if the kinds of integrals you want
> to solve are suitable for 'mellin', and use that instead.
>
> --
> Reid M. Pinchback
> Faculty Liaison
> Academic Computing Services, MIT
=================
It can do it, if you first tell it that z > 0. I.e.
> assume(z>0);
> int( exp(-t)*t^(z-1), t=0..infinity );
GAMMA(z~)
Here is the reason for this from my colleague
- --> Mike, you have to make sure that the Indefinite integral behaves well
at the origin. Take exp(-t) and expand in "t" then multiply this
result by t^(z-1). Then integrate term by term. What is the leading
term i.e. the smallest power in t? that's t^(z)/z. Right there must
be z<>0. If you include the origin i.e. t=0 then you must have z>0.
That's why z>0 is needed.
How do you know what you have to tell Maple to get it to give you
an answer? That's another problem. The only way to do this at the
moment is to trace the signum function -- which is called to compute
the sign of a constant during integration.
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