# Thread: Applying sequences to non-integers

1. Could I apply a sequential rule, for example , to non-integers like 4.9, 2.5, or ?

Or do I have to use the ceiling and floor functions?

2.

3. Hi Brody

You are actually approaching a rather interesting subject. Now there is no unique way to extend a function on the natural numbers to the integers, rationals, reals or complex numbers and a sequence is pretty much just a different way of writing a function on natural numbers.

However, that doesn't mean that there are not interesting ways to do the extension. For example, we know that the gamma function has the curious property that . This would suggest extending our function to this would suggest a reasonable interpretation of

Now whether this is enlightening or not depends on the context: some rather interesting mathematics can come out from silly substitutions like this. If you are curious you can take a look at Ramanujan's master theorem for example.

4. Thank you River Rat. I read about the Gamma and Pi functions for factorials. Very interesting.

The sequence I was using was for the purpose of finding values such as . Like a divisional form of factorials.

But it's interesting to me how . Unexpected, like

 Bookmarks
##### Bookmarks
 Posting Permissions
 You may not post new threads You may not post replies You may not post attachments You may not edit your posts   BB code is On Smilies are On [IMG] code is On [VIDEO] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are On Terms of Use Agreement