What does this Gothic W symbol mean?

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What on earth does this symbol mean here, in this article:

$$\mathfrak{W}(xe^x)$$

After copying and pasting, I find it is supposedly a W, but clearly it has a certain meaning since the article refers to W (Lambert W) and to this symbol very differently, as if it were a constant perhaps, or some function.

Not knowing what the authors mean by this is completely compromising my ability to understand this article!