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Re: Simplification with Integers assumption
*To*: mathgroup at smc.vnet.net
*Subject*: [mg74752] Re: Simplification with Integers assumption
*From*: dh <dh at metrohm.ch>
*Date*: Wed, 4 Apr 2007 03:53:50 -0400 (EDT)
*References*: <eunqc2$7ic$1@smc.vnet.net> <euqnsq$8cb$1@smc.vnet.net>
Sorry, I fooled myself by misstyping Element[x,Integers] instead of
Element[n,Integers].
With this corrected, I get for: Simplify[Sum[n!/(2*p)!/(n - 2*p)!, {p,
1, Infinity}], Assumptions -> n > 0 && Element[n, Integers]] zero, what
is obviously wrong.
Daniel
dh wrote:
> $Version 5.1 for Microsoft Windows (October 25, 2004)
>
>
>
> Hi,
>
> works o.k. in my version:
>
> Simplify[Sum[n!/(2*p)!/(n - 2*p)!, {p, 1, Infinity}], Assumptions -> n >
>
> 0] and Simplify[Sum[n!/(2*p)!/(n - 2*p)!, {p, 1, Infinity}], Assumptions
>
> -> n > 0 && Element[x, Integers]] give:
>
> -(((-2 + 2^n)*n!*Gamma[-n]*Sin[n*Pi])/(2*Pi))
>
> and with FullSimplify both give the simpler:-1 + 2^(-1 + n)
>
> Daniel
>
>
>
> did wrote:
>
>> On Mathematica 5.2 Windows, with the 4 similar commands:
>
>
>> Simplify[ Sum[ n! / (2*p)! / (n - 2*p)! , {p, 1, Infinity} ] ,
>
>> Assumptions -> n > 0]
>
>
>> FullSimplify[ Sum[ n! / (2*p)! / (n - 2*p)! , {p, 1, Infinity} ] ,
>
>> Assumptions -> n > 0]
>
>
>> Simplify[ Sum[ n! / (2*p)! / (n - 2*p)! , {p, 1, Infinity} ] ,
>
>> Assumptions -> n > 0 && n =E2=88=88 Integers]
>
>
>> FullSimplify[ Sum[ n! / (2*p)! / (n - 2*p)! , {p, 1, Infinity}] ,
>
>> Assumptions -> n > 0 && n =E2=88=88 Integers]
>
>
>
>> I get the different answers:
>
>
>> Out[1]= -(-2 + 2^n) n! Gamma[n] Sin[n Pi] / (2 Pi)
>
>
>> Out[2]= -1 + 2^(-1+n)
>
>
>> Out[3]= 0
>
>
>> Out[4]= 0
>
>
>> Outputs 1 & 2 look OK, but 3 & 4 are not. It seems that, with the
>
>> assumption n Integer,
>
>> Mathematica simplifies Sin[n Pi] by 0, omitting that Gamma[-n] is infinite.
>
>> Is it the expected behavior?
>
>
>> In this example, the simplest form can be obtained without imposing n
>
>> Integer (I
>
>> presume it's the correct answer), but in other situations it will be
>
>> required. What
>
>> is the safe way to do it?
>
>
>> Thanks
>
>
>
>
>
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