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From: Axel Vogt <&noreply@axelvogt.de>
Newsgroups: comp.soft-sys.math.maple
Subject: Re: Convert to factorial, bug?
Date: Mon, 2 Nov 2015 08:44:37 +0100
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On 01.11.2015 19:40, Peter Luschny wrote:
> A:=(n,k)->(n!/k!)*binomial(k,n-k)*2^(2*k-n);
> convert(A(n,k), factorial);
> B:=(n,k)->n!*2^(2*k-n)/((n-k)!*(2*k-n)!);
>
> A(1,0); # gives 0
> B(1,0); # Error, div by zero
>
> Peter
>

I guess that Maple uses 1 diveded by GAMMA and not the function 1/GAMMA,
which is holomorphic and zero in non-negative integers.

B(n,0) = 2^(-n)/(-n)! = 2^(-n)/GAMMA(-n+1)

To work around that weakness here one can use the limit to get the result:

'Limit(B(n,0), n=1)';  ``= %;  #convert(%, GAMMA);
value(%); # gives 0