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  • Convert to factorial, bug?

    From Peter Luschny@21:1/5 to All on Sun Nov 1 10:40:01 2015
    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

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  • From Axel Vogt@21:1/5 to Peter Luschny on Mon Nov 2 08:44:37 2015
    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

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  • From Peter Luschny@21:1/5 to All on Mon Nov 2 00:15:23 2015
    To work around that weakness here one can use the limit to get the result:

    Dear Axel,

    I do not think that anybody wants to 'work around this weakness'.

    At least I want be assured that converting a simple binomial formula
    leads to an *equivalent* factorial formula; otherwise to offer such
    a 'conversion' is not only meaningless -- it's a dangerous bug!

    Peter

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