  The purpose of this paper is to show three general formulas of three global
characteristic coefficients of Collatz function. The Collatz function is
defined by the following operation on an arbitrary positive integer if N is odd
multiply it by 3 and add 1 then the sum obtained is divided by 2, if N is even
divide it by 2. Based on the principle, we define the n-order function denoted
by T^n such as the different expressions of that function are results of
applying Collatz function n times to a natural numbers which are expressed in
well determined forms. Based on these expressions, we can characterize that
n-order function by three global characteristic coefficients. In the first, we
define these three global coefficients. Secondly, we show that each global
characteristic coefficient has a general expression as a function of n.
