Stirling formula ~ Factorial

stirling_formula.R

library(tidyverse)

stirling_formula <- function(n) sqrt(2*pi*n)*(n / exp(1))^n

x <- 1:10

breaks_log10 <- 1:10 %>% 
  map_dbl(~ 10^.x) %>% 
  map(~ .x*(1:10)) %>% 
  unlist()

tibble(
  x, 
  factorial = factorial(x),
  stirling = stirling_formula(x)
) %>% 
  ggplot(aes(x = factorial, y = stirling)) +
  geom_abline(slope = 1, intercept = 0, linetype = "dotted") +
  geom_label(aes(label = x)) +
  scale_x_log10(minor_breaks = breaks_log10) +
  scale_y_log10(minor_breaks = breaks_log10) +
  xlab("n!") + ylab("Stirling(n)") +
  ggtitle("Stirling formula ~ Factorial", 
          "√(2πn).(n/e)^e for n = 1:10")

stirling_plot.png