Implenting log-gamma using recursion

I am trying to calculate lgamma using recursion. But it does not work as expected and gives out Nan and -Inf. What could be the reason for this?

sum = 0
log_gamma_recursive <- function(n) {
  if(n == 1){
    return(1)
  }else{
    sum = sum + log(log_gamma_recursive(n-1))
    print(sum)
    return(sum)
  }
}#log 4  + log 3 + log 2 + log 1
log_gamma_recursive(5)

Three things wrong with the code:

1. sum should not be a global variable, because successive "external" calls will return an accumulated value
2. You add the log of the return value to sum. This will give a series of nested logs:
   • You get log 4 + log(log 3 + log(log 2 + log (log 1)))), which is obviously wrong
   • log(log 1) = log 0 which tends to negative infinity mathematically speaking, but the library may or may not categorize this as a valid input
3. log_gamma(1) is 0, not 1

With that in mind, try this:

log_gamma_recursive <- function(n) {
  if (n <= 1) {
    return (0)
  }else{
    sum = (log(n-1) + log_gamma_recursive(n-1))
    print(sum)
    return(sum)
  }
}