BUG: Docs (or implementation) for negative inputs to factorial2 are incorrect

Describe your issue.

The docstring for factorial2 says:

If n < 0, the return value is 0.

However directly below that in the code, we can see this is not the case for n==-1

if exact:
    if n < -1:
        return 0
    if n <= 0:
        return 1

This will give a value of 1 for factorial2(-1) (if exact is false, it returns 1.0).

The code could be made consistent with the documentation (either making the result for n==-1 be 0 or saying that for n<-1, factorial2 is 0).

Alternatively, the code could be adapted to perform the extended double factorial which allows for negative inputs.

Reproducing Code Example

scipy.special.factorial(-1)

Error message

None

SciPy/NumPy/Python version information

1.7.1 1.21.2 sys.version_info(major=3, minor=9, micro=7, releaselevel=‘final’, serial=0)

[j-bowhay]

I think this can be closed gh-15592 changed the docstring to match the implementation and gh-15600 is discussing the current inconsistencies and any possible extensions.

[AvinashDwivedi]

Hello is there someone who can guide me to solve this issue. I really want to do this, It will be my first contribution, Please guide me I’m a newbie