How do I add a link to an external published article in a comment? I don't see the edit frame with the link button. What is the syntax I can use? (I did search Meta but did not see ...!)
To make a link in a comment you can use the
[text](url) syntax. (And, of course, you can use simply a bare URL - but I assume you want something nicer. Having some description of a link is useful for the users reading the comment, too.) The same syntax is possible in posts. (Although in posts there are other possibilities how to use links. Moreover, when composing or editing a post, you can insert a link using the built-in editor.)
For example, the following syntax works both in a post and in comments:
Link to a question on meta: [Hyperlink in a comment?](https://meta.mathoverflow.net/q/5410) This looks probably slightly better than a bare URL: https://meta.mathoverflow.net/q/5410
In the first comment under this post you can see how this looks in a comment - it looks approximately like this:
(As pointed out by LSpice, MO links are usually expanded in a post to full title - so putting just
https://meta.mathoverflow.net/q/5410 in a post renders like this: Hyperlink in a comment?. However, this is not true for external links - and in the comments the link to MO posts are not changed in this way either. Comments have some special links called magic links; such as
[so], etc - they are expanded to a link with the full title of the site.)
- Help center: How do I format my posts using Markdown or HTML? - specifically the section "Comment formatting"
- Inline links in comments (Meta Stack Exchange)
- How do you cite a reference in a comment? and other posts linked there (Mathematics Meta)
- How do comments work? (Meta Stack Exchange) - the section "How can I format and link in comments?"
A basic information about formatting in comments is displayed after you click on "help" when you're in the window for posting a comment. (Similar screenshot can be found in this post.)
The above concerns using (inline) links in comments. Since you have explicitly mentioned a "published article" I will add that using the citation helper (in the editor) and then copy-pasting the result in a comment will not work the same way as in a post.
For example, this works in a post, but not in a comment:
<cite authors="Dashiell, F. K. jun.">_Dashiell, F. K. jun._, [**Isomorphism problems for the Baire classes**](http://dx.doi.org/10.2140/pjm.1974.52.29), Pac. J. Math. 52, 29-43 (1974). [ZBL0291.46021](https://zbmath.org/?q=an:0291.46021).</cite>
However, simply removing the parts with
</cite> yields a result which IMO looks acceptable in a comment.
_Dashiell, F. K. jun._, [**Isomorphism problems for the Baire classes**](http://dx.doi.org/10.2140/pjm.1974.52.29), Pac. J. Math. 52, 29-43 (1974). [ZBL0291.46021](https://zbmath.org/?q=an:0291.46021).
(I have used the format exactly the same as generated by the citation helper - of course, depending on personal preferences, I can imagine that some users might change it slightly.)