How do we calculate factorials for numbers with decimal places? [duplicate]
Solution 1:
factorial of fraction number are defind by gamma function as link is in comments
since
$n!=n\times (n-1)!$
$\Gamma(n)=(n-1)!$
$n!=n \cdot \Gamma(n)$
$\Gamma \left(\dfrac 12\right)=\sqrt\pi$
so$$1.5!= \left(\dfrac 32\right)!= \left(\dfrac 32\right) \cdot \left(\dfrac 12\right)!= \left(\dfrac 32\right) \cdot \left(\dfrac 12\right) \cdot \Gamma{\left(\dfrac 12\right)} = \dfrac 34 \sqrt \pi$$
this can be useful.