[R] help on using sum in writng a function again

[skim033 at student.ucr.edu]

Hi, thanks for your reply. 
Here I would like to ask you again more directly.
The following is what I had for now.
The function to begin with is 
dnorm(theta+2*pi*j,0,1)*(pnorm(((2*pi*(k+1)-rho*
(theta+2*pi*j)).

Now, I wanted to sum it over k from -10000 to 10000. So, I 
wrote the following.
f1<-function(theta,j){
aa<-seq(-10000,10000,lenght=20001)
sum(dnorm(theta+2*pi*j,0,1)*(pnorm(((2*pi*(aa+1)-rho*
(theta+2*pi*j))
}

Next, I would like sum over j as
(This is a way I thouhgt about computing a double sum)
f2<-function(theta){
aa<-c(-1,0,1)
sum(f(theta,aa))
}
expecting f2 be a function of theta. 

Then, I wanted to plot f2 for theta from 0 to 2*pi. But, f2
(seq(0,2*pi,length=10)) is a scalar, not a vector with the 
dimension of 10x1. I would like to ask you how I can use 
rowSums with outer or some other method to correct my coding.

I would like to thank you in advance.
Sungsu.
UC riverside.