(-π)!

Maybe

  (-π)! = (-3.1415926535897932384626433832795)! = -3.1909066873083528993320905932927


if this result is correct then

 What is the demonstration?

• No demonstration May 17, 2017 at 20:39

The factorial is usually considered to be defined only for natural numbers. One standard way to extend the definition of factorial outside this set is to consider the gamma function: $\Gamma (x+1) = x!$ when $x$ is a natural numbers but is also defined, for example, when $x=-\pi$. In fact, $\Gamma(-\pi+1)\simeq -3.19$. With a slight abuse of notation whoever our whatever told you that $(-\pi)!\simeq -3.19$ most likely adopted the extended definition provided by the gamma function.
But often, factorial notation is used to mean the gamma function rather than factorials: specifically, $n!$ is used to mean $\Gamma(n+1)$
• Note that $\Gamma(1-\pi)$ is roughly the RHS written down by the OP... May 17, 2017 at 19:19
The factorial function is generally understood to be defined only for the domain $\{0,1,2,\ldots\}$. However, it coincides with another function, the gamma function, which is defined for all real numbers except for non-positive integers. In particular, $n!=\Gamma(n+1)$. Thus, we could identify $(-\pi)!$ as $\Gamma(-\pi+1)$.