`zeta(0, x), zeta(s, -1)` gives wrong answer

[inkydragon]

We have: zeta(0, x) = 0.5 - x
Ref: https://en.wikipedia.org/wiki/Hurwitz_zeta_function#Negative_integers

But SpecialFunctions v2.5.1 gives:

julia> [ zeta(0, n) for n in 1:3 ]  # look good
3-element Vector{Float64}:
 -0.5
 -1.5
 -2.5

julia> [ zeta(0, -n) for n in 1:3 ]
3-element Vector{Float64}:
 0.5
 1.5
 2.5

julia> [ 0.5+n for n in 1:3 ]
3-element Vector{Float64}:
 1.5
 2.5
 3.5

And Wolfram gives:

In[2]:= Zeta[0, -1]
Out[2]= 3/2
In[3]:= Zeta[0, -2]
Out[3]= 5/2
In[4]:= Zeta[0, -3]
Out[4]= 7/2

---

Special values

Test with: zeta(s, -1) == 1 + zeta(s)
ref: https://reference.wolfram.com/language/ref/Zeta.html#479430652

julia> zeta(-9, -1)
-1.0075757575757576

julia> zeta(-7, -1)
-0.9958333333333333

julia> zeta(-6, -1)
NaN

julia> zeta(2, -1)
Inf

Wolfram:

In[10]:= Zeta[-9, -1]
Out[10]= 131/132
In[11]:= Zeta[-7, -1]
Out[11]= 241/240
In[12]:= Zeta[-6, -1]
Out[12]= 1
In[13]:= Zeta[2, -1]
Out[13]= 1+\[Pi]^2/6