WeberE definition from Wikipedia doesn't match the definition from Wolfram Language?

Question

According to Wikipedia - Struve function: Relation to other functions the WeberE function should return this, if the first argument is a negative integer:

$$ \mathbf{E}_{-n}(z) = \frac{(-1)^{n+1}}{\pi}\sum_{k=0}^{\left \lfloor \frac{n-1}{2} \right \rfloor} \frac{\Gamma(n-k-\frac{1}{2}) \left (\frac{z}{2} \right )^{-n+2k+1}}{\Gamma \left (k+ \frac{3}{2} \right)}-\mathbf{H}_{-n}(z) $$

But in Wolfram language it only returns a formula with an alternating sign from the corresponding positive integer argument?

>> Table[WeberE[n, z], {n, 1, 10}] == Table[(-1)^n*WeberE[n, z], {n, -1, -10,-1}]

True

Is the WeberE function for negative first integer argument defined different from the Wikipedia definition?

Update: the Wikipedia equation is edited now. See below

Answer 1

There is a mistake on Wikipedia the upper bound in the sum should be Ceiling[(n - 3)/2]}] instead of Floor[(n - 1)/2]. Please correct the Wikipedia page.

z = Sqrt[3];
N[Table[WeberE[-n, z] == (-1)^(n + 1)/π Sum[(Gamma[1 n - k - 1/2] (z/2)^(-n + 2 k + 1))/
      Gamma[k + 3/2], {k, 0, Ceiling[(n - 3)/2]}] - 
    StruveH[-n, z], {n, 1, 10}], 10]

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{True, True, True, True, True, True, True, True, True, True}