# Is there a standard name for functions of the form $x^\alpha p(x)$, where $p(x)$ is a polynomial?

Is there any existing standard terminology for functions of the form $x^\alpha p(x)$, where $p(x)$ is a polynomial and $\alpha$ is e.g. a complex number? I haven't been able to come up with any good name (e.g. generalised polynomial or near-polynomial don't sound so good), and no one I've talked to knows any standard terminology, so I thought I'd ask here.

Edit: the motivation for this is the following: if you have a polynomial solution $f(z)$ to a hypergeometric differential equation (i.e. some $_pF_q$ that is a polynomial), then $x^\alpha f(x)$ (for a certain given multiindex $\alpha$) is a solution to the associated GKZ $A$-hypergeometric system in $p+q$ variables. I'm currently working on generalising some results on polynomial solutions to the hypergeometric equation, and I'd like a good name for this kind of power-times-polynomial thing.

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Can you explain why you'd want such an object, rather than general linear combinations of $x^\alpha$s? –  Allen Knutson Jan 29 '13 at 17:10
Calling it a "power-times-polynomial" doesn't seem too painful, given that one doesn't expect to use the concept all that often. –  James Cranch Jan 29 '13 at 17:12
its just a fractional polynomial multiplied with an honest one :-) –  Suvrit Jan 29 '13 at 20:48
What about L$\alpha$urent polynomial? –  Martin Brandenburg Jan 30 '13 at 9:06