c - Stirling approximation producing a different output than expected -

so new c , learning syntax. have come across problem though. trying prove stirlings approximation where

ln (n!) = n ln (n) - (n)

so when make print statements within code test whether each element of array producing output of array number want be. it's far it.

#include <stdio.h> #include <stdlib.h> #include <math.h>  double * natural_log (); /* obtain natural log of 0 100 , store each value in array     */ double * approximation (); /* use sterling approximation caluculate numbers 0 - 100 , store in array */ double * difference (); /* calculate difference between arrays */ double * percentage (); /* calculate percentage of difference , return array */  int main () {    natural_log ();  /*  approximation (); */    return 0; }   double * natural_log () {      static double natural_array[101]; /* set array */     int i; /* set integer increase array value */       natural_array[0] = 0.0; /* set first value in array */     natural_array[1] = log(2);      double x;     x = natural_array [1];     (i = 2; <=100; i++) { /* set loop increment */         natural_array[i] = x + log(1 + i);         x = natural_array[i];         **printf ("element[%d] = %d\n", i, x);**      }     return natural_array; }  double * approximation () {      static double approximation_array[99]; /* set array */     int i;  /* set integer increase array value */      (i = 0; <=100; i++) {         approximation_array[i] = (i) * log(i) - (i);     }     return approximation_array; } 

with print statement in bold produces output

 element[2] = 688  element[3] = 2048  element[4] = 1232  element[5] = 688  .....  .....  element[100] = 544 

i these numbers it's not supposed spitting out on output can explain why is? thank you!

you not printing right data type with

printf ("element[%d] = %d\n", i, x); 

which wants print int type. please try

printf ("element[%d] = %e\n", i, x); 

you must declare array thus

static double natural_array[101]; 

either that, or reduce loop limit. better tie 2 perhaps this

#define elements 100 ... static double natural_array[elements];  ... (i = 2; < elements; i++) {      ...