discrete curve

A discrete function has values only for the natural numbers (n). Giving to the interval [n - 1/2, n + 1/2] the value of f(n), we get a bar formed curve, a histogram.
When the discrete function gives a percentage, and the function values have been ordered from high to low, the curve is called a Pareto diagram.

We shall see that some discrete curves for large n can be approached by (often exponential) continuous functions.

The following discrete curves can be distinguished:

• factorial
• prime related function
  • Euler's indicatrix
  • inverse prime summation
  • Möbius function
  • prime counting function
  • prime function
• (discrete) probability distribution
  The function gives the probability that a value n occurs. Simple functions are the univalent distribution (just one value) and the alternative distribution (two different values).
  Others distributions are:
  • binomial distribution density
  • Fermi-Dirac distribution
  • hypergeometric distribution
  • Poisson distribution