Re: Doublefactorial and Pochhammer

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From	Joe Riel <joer@san.rr.com>
Newsgroups	comp.soft-sys.math.maple
Subject	Re: Doublefactorial and Pochhammer
Date	Mon, 09 Nov 2015 15:44:00 -0800
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Peter Luschny <peter.luschny@gmail.com> writes:

> a := n -> doublefactorial(2*n-1)-2^n*pochhammer(1/2,n):
> seq(a(n), n=0..99);
> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
>
> a(100)
> 6666308670072953744411215006735034163324489389674388736363184954745922258576896518414625915283128424390474317708176893511841954015267176587405666801912441638268530971962511539459228515625-1267650600228229401496703205376*GAMMA(201/2)/sqrt(Pi)
>
> Can somebody explain this sudden jump?
>

GAMMA has a preset limit at which it will apply
a particular simplification to an integer input.
You can extend this by modifying a global constant:

`GAMMA/magic` := 2*`GAMMA/magic`:

a(100);
             0

The constant actually is an expression sequence of four integers.

-- 
Joe Riel

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Doublefactorial and Pochhammer Peter Luschny <peter.luschny@gmail.com> - 2015-11-05 15:00 -0800
  Re: Doublefactorial and Pochhammer jfh <john.harper@vuw.ac.nz> - 2015-11-05 16:05 -0800
    Re: Doublefactorial and Pochhammer Peter Luschny <peter.luschny@gmail.com> - 2015-11-06 00:40 -0800
  Re: Doublefactorial and Pochhammer Joe Riel <joer@san.rr.com> - 2015-11-09 15:44 -0800

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