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I'm thinking of the form

$$p_n = a_0t^0 + a_1t^1 + a_2t^2 +\cdots + a_nt^n.$$

However the only way I can think to write it is

$$p_n = p_{n-1}+ a_nt^n.$$

I'm probably thinking the wrong way. This "definition" wouldn't even define any numbers when used recursively, it would just show that there's some a $p_n$ with some coefficients $a_0, a_1,a_2, \ldots, a_n$. Or... maybe I'm doubting myself? I'm not sure.

1 Answers 1