# Is there a name for these polynomials?

Given $t \in \mathbb{R}[0,1]$, consider the following set of polynomials:

$$\left[-{\left(t - 1\right)}^{2} t, {\left(t - 1\right)} {\left(t^{2} - t - 1\right)}, -{\left(t^{2} - t - 1\right)} t, {\left(t - 1\right)} t^{2}\right].$$

They show up as the coefficients of an interpolation filter. I've put them in a form that reminds me of Bernstein polynomials. They sum to unity, but don't appear to be orthogonal on $[0,1]$. They might be with respect to some weight function (or other interval).

Other than digging through lists of various types of polynomials, I'm at a loss for terminology to use in searching for further information. Does anyone recognize these as being part of some larger class, regardless of their connection to interpolation?

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What particular interpolation filter? – J. M. Jul 17 '12 at 12:24
@J.M. From a cubic convolution kernel. I didn't post too much about the derivation, because I'm interested in the abstract form of the result (i.e. other ways to get there, if any). – datageist Jul 17 '12 at 16:11
Something something cubic spline, yes? Apparently a cardinal spline with tension $c=-1$. – Rahul Jan 6 '13 at 23:52
Something like that, IIRC. – datageist Jan 7 '13 at 5:15