> Every mathematician should know what polygamma function is. In fact somebody who does not know what it is, and is not professional enough to at least look up the definition in google, cannot be called a mathematician.

That is a nice addition to my (vast and versatile) collection of reasons why I cannot be called a mathematician. I have no idea what the polygamma function is and certainly have no desire to investigate it using google or Wikipedia. In general, the question boils down to "Whom are you writing your question/answer for: the few experts or the wide MO audience?" Both points of view have their merits. On one hand, why should one bother to explain things to people who have never been interested in the problem before it appeared on MO and will forget the whole thing as soon as they take their eyes from the screen? On the other hand, why should you give a public presentation when 90% of the public you address do not understand the language you speak? I guess, it is OK for you to make your choice of how to write, provided that you allow the public to make its choice of how to up/downvote afterwards and have no grudge if your post is rated not as high as you hoped for. If you care about your ratings, you have to adjust to the (different and contradictory) tastes of the surrounding people, not to try to change them. If you don't, you just do what you find most appropriate and ignore the feedback, whether positive or negative. If you are in between, do something in between. Trying to set up a general rule here is rather pointless and even if you do, most people (including myself) will just ignore it.

>Should I similarly downvote all questions which I do not understand?

Yes, if it is your firm opinion that the posts on public fora (math. or otherwise) should be made in the language understandable to most readers. No, if you don't hold such opinion. Up and downvoting is there merely to enforce the "consensus culture" of the forum. That culture is the combination of the viewpoints of different people that do not agree with each other. It would be useless to try to make me and you to agree on what is a good writing style in general (or to make any two other people agree on any universal rule) but if we both honestly provide our feedback using the voting system, and a third person cares about his ratings, in finite time he'll find a writing style that we both will approve of (though for completely different reasons) and that's all that is needed or that one can hope for.

> I guess, it is OK for you to make your choice of how to write, provided that you allow the public to make its choice of how to up/downvote afterwards and have no grudge if your post is rated not as high as you hoped for.

In that case we will end up in that questions about the field that are represented by the minority of audience harshly downvoted. This will become a war between branches of mathematics which will end in a victory of the side which has the majority.

To avoid this I suggest people just do not downvote what they do not understand, as I do.

@Anixx: I am pretty sure that fedja is a world class classical analyst. If he has never heard of the polygamma function, perhaps you should rethink your position and be willing to define terms that are unfamiliar to people who might give answers to your questions.

The polygamma function is found neither in the index of Special Functions by Andrews, Askey and Roy, nor in Whittaker and Watson, although the digamma function is in both (as "logarithmic derivate of Gamma function" in the latter).

Dan, not that I consider it important, but I was interested in seeing whether I would get the same results you got. If I enter "polygamma function" with quotes into Google, I get a little over 11000 hits; if I enter "compact closed category" with quotes, I get more than 25000. If I enter polygamma function without quotes, I get between 27000 and 28000 hits; if I try the same for compact closed category, I get over 43000000 hits.

How many Google hits are there for "threads that have outlived their usefulness on meta.mathoverflow.net"?

@dan: In order to understand a question about "compact closed categories" I would have to ask what they are. So, yes, the definition (or link to it) should be included in that question as well.