Re: Problem with plotting and simplifying a function
- To: mathgroup at smc.vnet.net
- Subject: [mg100626] Re: Problem with plotting and simplifying a function
- From: dh <dh at metrohm.com>
- Date: Tue, 9 Jun 2009 06:37:34 -0400 (EDT)
- References: <h0bu5u$8nt$1@smc.vnet.net>
Hi,
simply write:
Sum[Cos[2 Pi k t], {k, -n, n}]
this gives:
-1 + 2 Cos[n \[Pi] t] Csc[\[Pi] t] Sin[(1 + n) \[Pi] t]
Further, note that the Sin part is zero because Sin is an odd function.
Daniel
new one wrote:
> I have a question that troubles me , and I'll appreciate your advices.
> Given Sum of : X_N(t) =Sum [ Exp(j2*Pi*k*t) ] with lower limit -N and upper limit +N , -2<= t <= 2
> I need to calculate x(t) ,so I used Euler :
> X_N(t) = Sum e^(j2*pi*k*t) = Sum [ cos(2pi*k*t) + j*sin (2pi*k*t) ].
>
> Now ,if I'm mistaken the sinus part becom equal to zero , because the cycle
> of sinus is PI . But I have a problem with the Cosinus part , how can I
> simplify it ? the "t" parameter interrupts with the simplifying ......
> maybe separating it to conditions ? N=2R ------> even , N=2R+1 --> odd ?
>
> thanks in advance
>