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  • Doublefactorial and Pochhammer

    From jfh@21:1/5 to Peter Luschny on Thu Nov 5 16:05:24 2015
    On Friday, November 6, 2015 at 12:00:07 PM UTC+13, Peter Luschny wrote:
    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?

    Peter

    No, but I believe the answer from Maple 2015 because:

    simplify(%);
    0

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  • From Peter Luschny@21:1/5 to All on Thu Nov 5 15:00:05 2015
    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?

    Peter

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  • From Peter Luschny@21:1/5 to All on Fri Nov 6 00:40:44 2015
    Can somebody explain this sudden jump?
    No, but I believe the answer from Maple 2015 because:
    simplify(%);

    What I never have questioned. But there is not only
    the numerical data here.

    a := n -> 2^n*pochhammer(1/2,n):

    type(a(99),integer); -> true
    type(a(100),integer); -> false

    So if one relies on properties of integers they might totally
    unprepared disappear with unpredictable consequences.




    0

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  • From Joe Riel@21:1/5 to Peter Luschny on Mon Nov 9 15:44:00 2015
    Peter Luschny <[email protected]> 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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