What's the relation (IMPORTANT)?

1. Jan 27, 2006

TheDestroyer

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?

x->y

1->1

2->3/2

3->11/6

4->25/12

5->137/60

6->147/60

7->363/140

8->761/280

9->7192/2520

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

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• Graph1.GIF
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Last edited by a moderator: Feb 1, 2006
2. Jan 27, 2006

StatusX

Those look like the harmonic numbers:

$$H_n = \sum_{k=1}^n \frac{1}{k}$$

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
3. Jan 27, 2006

TheDestroyer

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?

4. Jan 27, 2006

StatusX

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

$$H_n = \gamma + \psi_0(n+1)$$

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

$$\psi_0(x) = \frac{\Gamma'(x)}{\Gamma(x)}$$

So the function:

$$f(x)=\gamma + \psi_0(x+1)$$

Is a continuous function which has the Harmonic numbers as its value at the positive integers.

5. Jan 27, 2006

D H

Staff Emeritus
Did you look at the link? The answer you want is there.

6. Jan 28, 2006

TheDestroyer

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
7. Feb 1, 2006

Hurkyl

Staff Emeritus
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.

8. Feb 1, 2006

TheDestroyer

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