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Two factorials  and  are the particular cases of the incomplete gamma function  with the second argument being  :
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.
The factorials and binomials  ,  ,  ,  , and  are interconnected by the following formulas:
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