Connections within the group of factorials and binomials and with other function groups

Representations through more general functions

Two factorials and are the particular cases of the incomplete gamma function with the second argument being :

Representations through related equivalent functions

The factorial , double factorial , Pochhammer symbol , binomial coefficient , and multinomial coefficient can be represented through the gamma function by the following formulas:

Many of these formulas are used as the main elements of the definitions of many functions.

Representations through other factorials and binomials

The factorials and binomials , , , , and are interconnected by the following formulas: