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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