Re: Difficult sum

From: Ioannis (morpheus_at_olympus.mons)
Date: 06/05/04 

Date: Sat, 5 Jun 2004 18:57:49 +0300

Ο "G. A. Edgar" <edgar@math.ohio-state.edu.invalid> έγραψε στο μήνυμα
news:050620040804033501%edgar@math.ohio-state.edu.invalid...
[snip]

> Instead of subtracting the two incomplete GAMMAs, why not use
> the definition and write the difference as:
>
> > GAMMA(n+1,-1/e)-GAMMA(n+1,1/e) = -Int(exp(-t)*t^n,t=-exp(-1)..exp(-1));
>
> exp(-1)
> /
> | n
> GAMMA(n + 1, - 1/e) - GAMMA(n + 1, 1/e) = - | exp(-t) t dt
> |
> /
> -exp(-1)
>
>
> That will be better for numeric computation, I think.
[snip]

Can you do that though? The definition I've heard is that for *Re(z)>0*,
GAMMA(n+1,z)=Int_z^oo exp(-t)*t^n dt.

Is it true that GAMMA(n+1,-1/e)=Int_{-1/e}^oo exp(-t)*t^n dt?

If it is, then it follows that

GAMMA(n+1,-1/e)-GAMMA(n+1,1/e)=Int_{-1/e}^{1/e}exp(-t)*t^n dt

Where did you get the "-" sign from?

Thanks,

> --
> G. A. Edgar
http://www.math.ohio-state.edu/~edgar/ 

--
Ioannis Galidakis
http://users.forthnet.gr/ath/jgal/
------------------------------------------
Eventually, _everything_ is understandable

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