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I'm not sure, but I think that the function

$_2F_1(-n,-m,;1;x)$

cannot be written through more elementary functions. Am I right? I am asking this as a non-mathematician.

Or in other way: Can above expression be treated as coefficient of $z^m$ in the product

$$ (1+xz)^n\,(1+z)^m.$$ say? (This has been the one answer on the related question Binomial series with two binomial coefficents)

I hope that I do not break any rule with posting like this.....

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    Relevant link: http://www.wolframalpha.com/input/?i=2F1%28-n%2C-m%3B1%3Bx%292012-10-20
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    Wj32, thanks a lot. Very useful link. :)2012-10-20

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