The authors make no mention whatsoever about...
Is this sentence appropriate for formal writing?
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Whatsoever is perfectly fine if used for emphasis. For example, if you were reviewing a book about desserts, you might say:
The authors make no mention about ice cream.
This is a plain statement, just reporting the facts. Nothing wrong with that. But you might want to go at the matter a little harder.
The authors make no mention whatsoever about ice cream.
This is emphatic, emphasizing the writer's disbelief or disappointment that the authors did not mention ice cream. Probably this writer had hoped a written work about dessert would at least mention ice cream.
There are other constructions you could use for emphasis as well.
The authors make no mention at all about ice cream.
The authors make no mention whatever about ice cream.
The authors make no mention in 547 pages about ice cream.
And so on. The point is, sometimes extra words are fine to use when making a point. And, yes, I like ice cream and would be indignant if a book about dessert were to leave it out.
I think in that context whatsoever is unnecessary and perhaps seems slightly condescending, as though you're deriding them for not mentioning whatever it is.
The authors make no mention of X works perfectly well without the added emphasis.
Still, I wouldn't necessarily have said that whatsoever is informal per se.