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New entry special function, extensions to hypergeometric function, Selberg integral. New entries gamma function, recently also Euler beta function.
Stub for elementary function.
At elementary function, I’ve never seen ’transcendental’ defined that way; I thought that meant a function that isn’t algebraic, e.g., $e^x$ or $\sin(x)$. I can’t remember seeing anything other than ’non-elementary’ (or something similar) for a function not in the class of elementary functions.
I changed the title from ’gamma function’ to Gamma function, and added some material.
You are right about transcendental ! This way as you say is used by algebraic geometers, and this is now dominant. In special functions, it was sometimes in earlier times used the way I said, but the algebraic geometry usage is now far dominant. It should be corrected.
For Gamma vs. gamma I would not quite agree. Some of the modern monographs on special functions which I read these days use gamma and beta when spelling the name in full, without capitals. In fact I do not recall ever seen it other way around. This has nothing to do with the capitalization of the notation, which is pretty consistent for gamma and inconsistent for Euler beta in the literature. Of course, following the notation in spelling has some information and is not a bad idea.
I hope we will have much more in those entries in $n$Lab soon…
You’re probably right about Gamma/gamma – I was looking quickly at Andrews-Askey-Roy and see they have Gamma in chapter/section titles, but gamma within the text (I haven’t gone through this super-carefully). I thought Gamma was more logical, but I’ll leave it for you to decide. Sorry for the change!
Arguably, the proper name is ‘$\Gamma$ function’ and our naming conventions then require us to put the page at Gamma function as the nearest approximation without special characters.
I do not know of “arguably” argument in recording the language conventjons. The way the language is it is. the name gamma function is used when the spelling is in full, i.e. in primary form. Calling it $\Gamma$-function is just an abbreviation.
sin² x + cos² x = 1, and surely linear combinations count…
Come on, multiplication with a scalar is an algebraic operation.
I’ve gone ahead and included the constant functions in the article, to remove any doubt. (The article hadn’t included multiplication by a scalar, which of course should be there.)
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