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  1. Reply/View Conversation
    Hey Balarka, Daniel is upgrading the forum software to a completely new platform. It should be back up soon.
  2. Reply/View Conversation
    I agree that fun shouldn't introduce wrong concepts.

    PS: Yes, I'll add one when I start the next post.
  3. Reply/View Conversation
    Ok, then you are looking at rigor but as I said these tutorials will be for fun. I want a high school student to understand it. It would be great to have your comments when I start posting bout that, though. I know I can learn from you as I am haven't read that much about these concepts.
  4. Reply/View Conversation
    What is your definition of Regularization ?
  5. Reply/View Conversation
    We can extend the zeta function to analytic function in the whole complex plane except at 1. By definition we have
    $$\zeta(s) =\sum \frac{1}{n^s}$$
    So zeta on the left is analytic for all $s \neq 1$ but the sum on the right does only converge for $Re(s) >1$.
    So the analytic continuation of zeta has enabled us to give values to the divergent sum on the right.
  6. Reply/View Conversation
    Hey Balarka , the idea of regularization is giving a finite value for divergent series or integrals. Consider the following
    $$\zeta(-2)= 0 $$
    $$1+4+9+\cdots = 0 $$
  7. Okay, thanks. I think the former one is just what I wanted.
  8. Reply/View Conversation
    Hey Balarka, I do not know of a closed for that sum. But there are some identities related to this problem:
    $$
    \begin{align*}
    \sum_{k=1}^p \frac{H_k^{(2)}}{k}+\sum_{k=1}^p \frac{H_k}{k^2} &= H_p^{(3)}+H_p^{(2)}H_p \\
    \sum_{k=1}^p \frac{H_k^{(2)}}{k}+\sum_{k=1}^p \frac{(H_k)^2}{k} &= \frac{(H_p)^3+3H_p H_p^{(2)}+2H_p^{(3)}}{3}
    \end{align*}
    $$
    To prove these, we can use induction.
  9. Reply/View Conversation
    Possibly, that's my name there. I don't gravitate toward your usual tags, I suppose. I'm more in multivariable calculus, calculus and lower level ones.
  10. Reply/View Conversation
    Good question , where did you get that ? I never tried something similar but surely I will give it a shot !
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About mathbalarka

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Date of Birth
January 12, 2000 (17)
About mathbalarka
Biography:
I know a thing or two about topology. Find number theory interesting but don't know much about it.
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West Bengal, India
Interests:
Number Theory
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India

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Some of my notes on number theoretic topics are on a few primality tests and on Hardy & Littlewood's result (incomplete). The other articles are on quintics : about a brief description of Kiepert algorithm and a short introduction on quintic-solving algorithms, respectively. I have also written up an introductory thread on Riemann Hypothesis

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Name: Graduate POTW Award (Jul-Dec 2013)
Issue time: January 5th, 2014 16:52
Issue reason:
Math Help Boards