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 > > > > >