Exponential family
What is important to note, and what characterizes all exponential family variants, is that the parameter(s) and the observation variable(s) must factorize (can be separated into products each of which involves only one type of variable), either directly or within either part (the base or exponent) of an exponentiation operation. Generally, this means that all of the factors constituting the density or mass function must be of one of the following forms:
Exponentiation
Another characterization of the exponential function formula_66 is as the limit of formula_75, as "n" approaches infinity. By thinking of the "n"th power in this definition as repeated multiplication in polar form, it can be used to visually illustrate Euler's formula. Any complex number can be represented in polar form as formula_76, where "r" is the absolute value and "θ" is its argument. The product of two complex numbers formula_77 and formula_78 is formula_79.