! (factorial)

Syntax

expression !

Domain

| : ( R \ Z- ) -> R

Example

-2.1! = 9.71

Description

The factorial for an integer value is the product of all integers preceding it. By definition, 0! = 1.

The Expression Calculator calculates factorials using the Euler's Gamma function, which allows a negative extension and factorials of any rational number except for negative whole numbers (Z-). A step of 0.01 is used to calculate the integral and infinity is replaced by a progressive algorithm.

x ! = Gamma( x + 1 )

Try plot(x!,x,-5,4) to see various values of the factorial and notice that it diverges to infinity for values in Z-.