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When answering this question, I give a link to a Google Books excerpt, where one can find almost exactly the function the OP is looking for. As it's only an excerpt, I guess it's fine to give the link. Sadly, not everybody can read it. Of course, I can make an image copy of the proof, and I already sent it to one user. But I can't send this to every reader.

So my question is: would it be permitted to rewrite the proof in LaTeX in my answer? Is it violation of copyright? I fear it is, but I'd like to be sure.

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    $\begingroup$ These two older discussions show that people have been occasionally doing exactly what you describe: meta.math.stackexchange.com/questions/1805/… and meta.math.stackexchange.com/questions/2600/… $\endgroup$
    – Martin Sleziak
    Dec 26, 2013 at 15:01
  • $\begingroup$ Thanks for the links. Actually, I'm not sure it addresses my main concern: in case it's not "fair use" to put a copy from Google Books (it's 3 pages here, I have put them, so you can check), is it ok to rework everything in LaTeX? $\endgroup$
    – Jean-Claude Arbaut
    Dec 26, 2013 at 15:32
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    $\begingroup$ I think what you have done is ok - you have explicitly mentioned that you are not sure whether it is fair use and that if someone thinks it is not ok, they should say so. My opinion is that it would be ok if you add LaTeX-ed transcription. $\endgroup$
    – Martin Sleziak
    Dec 26, 2013 at 15:43

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Copyright law governs the right to make copies and "derivative works" of original works. Making an unauthorized image of pages from a copyrighted book would be a violation.

However copyright law does not protect the underlying ideas from "copying". You are allowed to express the ideas of a copyrighted work in your own words (or mathematical formulas).

I'm not a lawyer, but we do have an obligation to understand and follow the law. So my advice is offered as a colleague/community member. Providing a link to Google books is okay, but the pages may not be visible in some countries precisely because the copyright law outside the US pretty uniformly lacks a "fair use" exemption for reproducing small amounts of a copyrighted work for a non-commercial purpose (I'm condensing a complex legal doctrine here).

As an international resource StackExchange in general (and Math.SE in particular) should be conservative with respect to asserting any "fair use" justification for image copying. Accordingly I think arbautjc should remove the images until time is found to restate the idea of the function "in your own words", leaving for now only a link to Google books or some other resource on the web, such as a legitimately posted paper or class note.

Faculty pages and arXiv.org are often good places to find such resources.

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    $\begingroup$ Ok, I have removed the image. Well, actually only hidden for now, I'll rework it "in my own words" this week-end. Thanks for the advice, you have written what I had in mind, without being able to phrase it accurately. $\endgroup$
    – Jean-Claude Arbaut
    Dec 27, 2013 at 13:11
  • $\begingroup$ Hmmm ... you "rework it in your own words" and don't give a reference to where you got it? Sounds like plagiarism. Which, I guess, is not illegal. $\endgroup$
    – GEdgar
    Dec 27, 2013 at 14:46
  • $\begingroup$ @GEdgar: I'm not sure what you mean. The OP gave the names of the book and authors in the first sentence of his Answer, as well as the link via Google Books where you can find more information (bookstores and libraries that have the book, if you are so inclined). $\endgroup$
    – hardmath
    Dec 27, 2013 at 15:37
  • $\begingroup$ True. I just emphasize that one should cite the source. $\endgroup$
    – GEdgar
    Dec 27, 2013 at 17:27
  • $\begingroup$ @GEdgar I am aware of that, and as noticed by hardmath, there is already a reference. I have of course never considered to remove it. Even without regard to the fact that I use it (hence I cite), it seems to be a very good reference to give to the reader. $\endgroup$
    – Jean-Claude Arbaut
    Dec 27, 2013 at 18:48

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