In a publication, should an `\ldots` always be followed by a period?

I believe papers in English should be written in full and correct English sentences, with any mathematical formula being part of a sentence. Therefore, I believe that the correct form in this case would be

we have $\pi=3.1415\ldots\;$. However,

-- not

we have $\pi=3.1415\ldots$ However,

(and not

we have $\pi \approx 3.1415\ldots\;$. However,

).

(I inserted an instance of \; after \ldots, trying to improve the spacing.)

The principle mentioned by Iosif Pinelis that equations should follow the rules of grammar suggests to look at the OP in the broader context of the use of ellipsis in text: is $\ldots$ to be followed by a full stop period $.$ or not ?

The answer is "no" for British English (at least according to the University of Oxford Style Guide). For American English the answer is "yes" (at least for legal writing).

There are two possible correct answers.

• The first one the the mathematician's: the ellipsis for some implied content thing that isn't written, while the full stop marks the end of a sentence. Since each of the two typographical signs has its own functions, both should be present. This is logically correct, but typographically wrong. :)

• The second one is the typographer's, and it is better illustrated by the following three situations:

  1. Whenever a sentence contains an ellipsis right before the full stop, the full stop is no longer written.
  2. Whenever a sentence ends with an abbreviation (containing dots, such as "U.S.A." or "etc."), the full stop is no longer written (see also the links therein).
  3. Whenever a sentence ends with a quotation that itself ends with a full stop, the "outer" full stop is no longer written (it is a matter of debate, though, whether the remaining full stop should be inside or outside the quotation marks). Follow the links in the answers given here and see also this answer citing the Chicago Manual of Style.

To conclude, whenever a full stop would logically follow another typographical sign that itself ends with a dot, the full stop is no longer written (it "fuses" with the one preceding it).