Category:Simpson's Dissection

This category contains pages concerning Simpson's Dissection:

Let $\omega = e^{2 i \pi / q}$ be a primitive $q$th root of unity.

Let $p \not \equiv 0 \pmod q$.

Let:

$\ds \map f x = \sum_{n \mathop = 0}^\infty a_n x^n$

Then:

$\ds \sum_{n \mathop = 0}^\infty a_{n q + p} x^{n q + p} = \dfrac 1 q \sum_{j \mathop = 0}^{q - 1} \omega^{- j p} \map f {\omega^j x}$