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What's the relation (IMPORTANT)?

  1. Jan 27, 2006 #1
    What's the relation (IMPORTANT)??

    Hi guys, let me introduce my self, i'm a physicist studying in the university of aleppo...

    I want the relation between those number as a continuous function, my head is gonna blow !!! i can't find it, can any one help?











    hint: I can see that every number (y) is multiplied by 1/x

    PLEASE, I don't want any approximation, interpolation or anything like that cuz i can do it alone, i need an exact function

    for example, beta, gamma, airy, fresnels s and c, hermite, legender, or anything else BUT PLEEEEASE AN EXACT FUNCTION,

    I've attached the graph of this damn function

    It's not an easy question, i don't think i'm receiving an answer before 10 years, lol !!!

    Thanks Guys

    Attached Files:

    Last edited by a moderator: Feb 1, 2006
  2. jcsd
  3. Jan 27, 2006 #2


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    Homework Helper

    Those look like the harmonic numbers:

    [tex]H_n = \sum_{k=1}^n \frac{1}{k} [/tex]

    I don't believe there is an explicit formula for the nth term, but I could be wrong.

    EDIT: I'm sorry. Apparently there is one, although I don't know how useful it would be to you. See the mathworld article on harmonic numbers.
    Last edited: Jan 27, 2006
  4. Jan 27, 2006 #3
    Thank you, but i wanted it as a CONTINUOUS FUNCTION, not as a sum, integrals can be accepted as i mentioned above, thanks anyway for the link, any other ideas?
  5. Jan 27, 2006 #4


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    Homework Helper

    Well, as the link mentions, the Harmonic numbers are given by:

    [tex]H_n = \gamma + \psi_0(n+1)[/tex]

    where [itex]\gamma[/itex] is the Euler-Masceroni constant and [itex]\psi_0(x)[/itex] is the digamma function, related to the gamma function [itex]\Gamma(x)[/itex] by:

    [tex]\psi_0(x) = \frac{\Gamma'(x)}{\Gamma(x)}[/tex]

    So the function:

    [tex]f(x)=\gamma + \psi_0(x+1)[/tex]

    Is a continuous function which has the Harmonic numbers as its value at the positive integers.
  6. Jan 27, 2006 #5

    D H

    Staff: Mentor

    Did you look at the link? The answer you want is there.
  7. Jan 28, 2006 #6
    Sorry, The time was 2 am, and i saved the link and went to bed, thank you guys, i got what i want

    Thanks again
    Last edited by a moderator: Feb 1, 2006
  8. Feb 1, 2006 #7


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    Staff Emeritus
    Science Advisor
    Gold Member

    I've edited the original post (and the subthread related to what I cut out) in the hopes that I don't have to lock this.
  9. Feb 1, 2006 #8
    LOL !!! Why should you Hurkyl?? we didn't do anything wrong, did we? it's just a discussion about sciences !!!!!!!!!!!!!!!!!!!!!!!!!!
    Last edited: Feb 1, 2006
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