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Thread: Applying sequences to non-integers

  1. #1 Applying sequences to non-integers 
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    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?


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  3. #2  
    Forum Professor river_rat's Avatar
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    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.


    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  4. #3  
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    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
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