Currently, math.factorial only supports integers and not floats, whereas the "mathematical" version supports both integers and floats.
I.e:
```
import math


def better_factorial(n):
    return n * math.gamma(n)

print(math.factorial(10) == better_factorial(10))
```

This ends up in `True`, as that's correct.
However, `math.factorial(math.pi)` (for example, or any float)
Ends up in `ValueError: factorial() only accepts integral values`.
unlike `better_factorial(math.pi)` which would end up in 7.188082728976031.

My proposal is to make another function for floats, or even use the same math.factorial function and check inside it whether the given input is an integer or a float object.

SymPy has a symbolic factorial function that does this:

>>> import sympy as sym
>>> sym.factorial(10)
3628800
>>> sym.factorial(0.5)
0.886226925452758

If you pass in exact rational input then you can compute the result to any desired precision:

>>> sym.factorial(sym.Rational(1, 2))
factorial(1/2)
>>> sym.factorial(sym.Rational(1, 2)).evalf(60)
0.886226925452758013649083741670572591398774728061193564106904

Doing the same with integer values requires using evaluate=False to avoid the potentially slow exact integer calculation:

>>> sym.factorial(20)
2432902008176640000
>>> sym.factorial(20, evaluate=False)
factorial(20)
>>> sym.factorial(20, evaluate=False).evalf(10)
2.432902008e+18
>>> sym.factorial(10**30, evaluate=False).evalf(10)
6.223112323e+29565705518096748172348871081098

--

Oscar