[R] A question on summation of functions

[Liqiu Jiang]

Dear Rers,
 I am trying to do a 2 dimmensional intergration for a
function. the function is summation of another
function evaluated at a  series of vector values. I
have difficulty to code this function. 
 
For example: I have function f which is a bivariate
normal density function:


#define some constants
err<-0.5
m<-5
times<-seq(0, m-1)
rou<-sum(times)/sqrt(m*sum(times^2))
sig.w<- sqrt(m*err)
sig.wt<-sqrt(sum(times^2)*err)


#bivariate normal density 
f<-function(x, y, u.x, u.y)
exp(-((x-u.x)^2/sig.w^2+(y-u.y)^2/sig.wt^2-2*rou*(x-u.x)*(y-u.y)/(sig.w*sig.wt))/(2*(1-rou^2)))/(2*pi*sig.w*sig.wt*sqrt(1-rou^2))

###

I would like to have a function g which is defined as
######
uw = 1:n
uwt = (n+1):2n

g = function(x, y) f(x,y, uw[1], uw[1])+f(x,y, uw[2],
uwt[2])+
...+f(x,y, uw[n], uwt[n])
#######
if n is very large, I am not able to write all them
down, How can I code the function g. Thank you for
your consideration. 

Best wishes,
Liqiu