r - Recursive sum, using Poisson distribution -

i trying build recursive function in r,

h(x,t) = \sum\limits_{d=0}^{x} (pr(d=d)*(h*(x-d)+h(x-d,t-1)))  + \sum\limits_{d=x+1}^{\infty} (pr(d=d)*(p(*d-x)+ h(0,t-1))) 

where h,p constants, d ~ po(l) , h(x,0) = 0, code have done far, gives obvious error, can't see fix. code

p<- 1000 # unit penalty cost lost sales h<- 10 # unit inventory holding cost pr. time unit l<- 5 # mean of d h <- function(x,t){   if(t==0)(return(0))   fp <- 0   sp <- 0   for(d in 0:x){     fp <- fp + dpois(x=d,l)*(h*(x-d)+h(x-d,t-1))   }   for(d in x+1:inf){     sp <- sp + dpois(x=d,l)*(p*(d-x)+h(0,t-1))   }   return(fp+sp) } 

when run this, error is

error in 1:inf : result long vector 

which, seems obvious, question is, can point me in direction redefine problem, can r bring me solution?

thanks in advance.

going x+1:inf won't work. since you're using poisson's pdf, can add upper bound (why? think shape of pdf , how small values @ right tail):

for(d in x+1:100)

which when ran h(20,2) gives

[1] 252.806 

when increase

for(d in x+1:500)

then h(20,2) gives

[1] 252.806