Polynomials Extended

Question

What is the name of an more extended polynomial?

With parameters $\alpha = \{1,2,3,4,5,6,7\}$

$P_{n}(x) = \sum_{i=0}^{2n} \alpha_{i}x^{n-i}$

Example of 3rd order:

$P_{3}(x) = x^3 + 2x^2 + 3x + 4 + \frac{5}{x} + \frac{6}{x^2} + \frac{7}{x^3}$