Proof of Decreasing Exponential Factorials properties

• May 1st 2011, 06:44 AM
greenday1209
Proof of Decreasing Exponential Factorials properties
I need help checking the following properties (whether they're true or false):

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

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

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

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

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

• May 1st 2011, 10:10 PM
CaptainBlack
Quote:

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

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

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

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

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

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