In my post on hypertetrahedral polytopic roots, I gave a few formulae for functions such as the *triangular root*.

Here I give some very similar formulae for some *falling* and *rising roots*.

The notations for rising and falling factorials or powers are, respectively:

where

For example:

If then , and so (inventing some notation):

.

Similarly

.

Recall that

.

It is easy to see that these are related: this is because

Likewise,

hence

.

We also have that

hence

.

From these together with my earlier post, we therefore have, for example:

where

and:

Similarly the other formulae given in that earlier post give rise easily to a few further formulae.

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This entry was posted on Friday, 8 May 2009 at 00:41 and is filed under Mathematics, Research. You can follow any responses to this entry through the RSS 2.0 feed.
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