Is this a bug? Or there might be something I don't understand.
In[1]:= Multinomial[-1/2, -1/2, 1]
"During evaluation of In[1]:= Infinity::indet: Indeterminate expression 0 ComplexInfinity encountered."
Out[1]= Indeterminate
None of the arguments are located at poles of the factorial function (negative integers), so I expected this answer:
In[2]:= (-1/2 - 1/2 + 1)! / ((-1/2)! (-1/2)! (1)!)
Out[2]= 1/Pi
Checking with Simplify using Assumptions:
In[3]:= Assuming[a == -1/2 && b == -1/2 && c == 1,
Simplify[ Multinomial[a, b, c] == 1/Pi ]
]
Out[3]= True
Thanks! (I'm running 11.2)
In[4]:= $Version
Out[4]= "11.2.0 for Mac OS X x86 (64-bit) (September 11, 2017)"