Describe your issue.

The Hurwitz zeta function at 1/2, 1 is equivalent to Riemann zeta function at 1/2 and so zeta(1/2, 1) = zeta(1/2) = -1.46... (See WolframAlpha) but scipy.special.zeta returns nan. This may be expected behavior but if so it would be nice to have documentation for this behavior.

Related issue: pytorch/pytorch#68110

Reproducing Code Example

from scipy.special import zeta

# correct
output = zeta(1 / 2)
print(output)

# wrong
output = zeta(1 / 2, 1)
print(output)

Error message

-1.4603545088095866            
nan

SciPy/NumPy/Python version information

1.7.1 1.21.2 sys.version_info(major=3, minor=9, micro=8, releaselevel='final', serial=0)