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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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  • $\begingroup$ Can you explain why you'd want such an object, rather than general linear combinations of $x^\alpha$s? $\endgroup$ Jan 29, 2013 at 17:10
  • $\begingroup$ Calling it a "power-times-polynomial" doesn't seem too painful, given that one doesn't expect to use the concept all that often. $\endgroup$ Jan 29, 2013 at 17:12
  • $\begingroup$ its just a fractional polynomial multiplied with an honest one :-) $\endgroup$
    – Suvrit
    Jan 29, 2013 at 20:48
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    $\begingroup$ What about L$\alpha$urent polynomial? $\endgroup$ Jan 30, 2013 at 9:06

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