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A Theorem About Differenciation

  1. Jun 3, 2012 #1
    The above is not a spelling mistake as I am referring to differenciation rather than differentiation. As to the best of my knowledge, no one else has used the same term nor developed a similar method; and so I claim it as my own till challenged.
    Using differenciation, one can verify the expression of any finite polynomial.

    I put a lot of work in trying to write up an explanation for my method...so it's best seen in the word document attached. But I still don't think it's perfect.
    Please post your views and understanding of this. I would like any feedback.
     

    Attached Files:

  2. jcsd
  3. Jun 3, 2012 #2

    Hurkyl

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    I can't figure out what this sentence is supposed to mean.



    I haven't tried downloading your zip file. I'm guessing you're reproducing the theory of difference equations, or possibly have rediscovered some form of Newton series.
     
  4. Jun 3, 2012 #3
    Yes; it is the Newton series....but in a primitive form. Thanks for telling me. I didn't know how to search for it or identify it.

    That sentence means that you can use the Newton series method to check the formula for any function; assuming it is a finite polynomial and has rational inputs and outputs.
    For example, the sum of natural numbers. If one didn't know any theory behind the derivation; this method could yield n^2 /2 +n/2 by calculation with minimum logic involved.
    So simple that a computer could derive the formula.

    Thanks again for identifying it! I was hoping I was the first...but I guess Newton bet me! :)
     
  5. Jun 5, 2012 #4

    Hurkyl

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    I've looked at the article, I'll say it's much better written than I expected from a *.doc file posted on the internet!

    There's no better way to understand (and to eventually further) a subject than to derive it for yourself, so hopefully you'll continue your study / research, and a lead on existing knowledge will surely help. Sometimes just having good notation makes all the difference!

    If nothing else, I think differences are fun -- and the fact of analogies with differentials is interesting -- although I've only spent a little bit of time with them. And they certainly can be very useful in discrete math.
     
  6. Jun 7, 2012 #5
    Thanks! I actually used the latest Word 2007 to design the document, and then converted it into the old format for uploading.
     
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