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Simplification with Integers assumption
*To*: mathgroup at smc.vnet.net
*Subject*: [mg74709] Simplification with Integers assumption
*From*: "did" <didier.oslo at hotmail.com>
*Date*: Sun, 1 Apr 2007 04:19:44 -0400 (EDT)
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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