# Thread: Proof of Decreasing Exponential Factorials properties

1. ## Proof of Decreasing Exponential Factorials properties

I need help checking the following properties (whether they're true or false):

$\displaystyle x^{\underline{m.n}} = \prod_{k = 0}^{m-1} (x - kn)^\underline{n}$

$\displaystyle x^{\underline{m.n}} = \prod_{k = 0}^{n-1} (x - km)^\underline{n}$

$\displaystyle x^{\underline{m.n}} = \prod_{k = 0}^{n-1} (x - km)^\underline{m}$

where $\displaystyle x^{\underline{m.n}}$ is a decreasing factorial exponential, i.e.:

$\displaystyle x^{\underline{m.n}} = \prod_{k = 0}^{m.n - 1} (x-k)$

2. Originally Posted by greenday1209
I need help checking the following properties (whether they're true or false):

$\displaystyle x^{\underline{m.n}} = \prod_{k = 0}^{m-1} (x - kn)^\underline{n}$

$\displaystyle x^{\underline{m.n}} = \prod_{k = 0}^{n-1} (x - km)^\underline{n}$

$\displaystyle x^{\underline{m.n}} = \prod_{k = 0}^{n-1} (x - km)^\underline{m}$

where $\displaystyle x^{\underline{m.n}}$ is a decreasing factorial exponential, i.e.:

$\displaystyle x^{\underline{m.n}} = \prod_{k = 0}^{m.n - 1} (x-k)$