incorrect first moment of non central t-distribution

My issue is about the calculation of the first moment in t-distribution, which is wrong. I’m following the tutorial example from https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.t.html. By directly implementing the formula from wikipedia (https://en.wikipedia.org/wiki/Noncentral_t-distribution) I get a different result than through the scipy package. It seems that the first moment is always equal to the specified location (loc parameter).

Reproducing code example:

import numpy as np
from scipy.stats import t
from scipy.special import gamma

df = 10
loc = 1

scipy_first_moment = t.stats(df = df, loc = loc, moments='m')
real_first_moment = loc*np.sqrt(df/2)*(gamma(0.5*(df-1))/gamma(df/2))

print(scipy_first_moment == real_first_moment)

Error message:

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  ...

Scipy/Numpy/Python version information:

[rlucas7]

I agree w/ @josef-pkt If it starts to come up more frequently we can always revisit.

[josef-pkt]

note in the docstring, We cannot identify when a user doesn’t interpret the parameters correctly.

(twice in a row in 11 years is not a whole lot)