Facebook Page
Twitter
RSS
More Activity

73 Visitor Messages

  1. Reply/View Conversation
    Yes, you are correct. The first post in a thread may be edited within 2 hours, and all other posts within 24 hours.

    However, if you run over the 24 hour limit, I will lift the limit for you temporarily since you are adding such great content.
  2. Reply/View Conversation
    Hey Balarka, according the the settings in the ACP it is 5 minutes.
  3. Reply/View Conversation
    Hey Balarka, Daniel is upgrading the forum software to a completely new platform. It should be back up soon.
  4. Reply/View Conversation
    I agree that fun shouldn't introduce wrong concepts.

    PS: Yes, I'll add one when I start the next post.
  5. 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.
  6. Reply/View Conversation
    What is your definition of Regularization ?
  7. 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.
  8. Reply/View Conversation
    Hey Balarka , the idea of regularization is giving a finite value for divergent series or integrals. Consider the following
    $$\zeta(-2)= 0 $$
    $$1+4+9+\cdots = 0 $$
  9. Okay, thanks. I think the former one is just what I wanted.
  10. 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.
Showing Visitor Messages 21 to 30 of 73
Page 3 of 8 FirstFirst 12345 ... LastLast
Page 3 of 8 FirstFirst 12345 ... LastLast
About mathbalarka

Basic Information

Date of Birth
January 12, 2000 (18)
About mathbalarka
Biography:
I know a thing or two about topology. Find number theory interesting but don't know much about it.
Location:
West Bengal, India
Interests:
Number Theory
Country Flag:
India

Signature


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

Statistics


Total Posts
Total Posts
573
Posts Per Day
0.30
Thanks Data
Thanks Given
699
Thanks Received
1,378
Thanks Received Per Post
2.405
Visitor Messages
Total Messages
73
Most Recent Message
June 6th, 2018 01:03
General Information
Last Activity
June 6th, 2018 01:06
Last Visit
June 6th, 2018 at 01:06
Last Post
January 1st, 2017 at 22:39
Join Date
March 22nd, 2013
Referrer
MarkFL
Referrals
2
Referred Members
neelmodi, zuby

17 Friends

  1. agentmulder Offline

    MHB Apprentice

    agentmulder
  2. Albert Offline

    MHB Master

    Albert
  3. Bacterius Offline

    MHB Journeyman

    Bacterius
  4. evinda Offline

    MHB Master

    evinda
  5. Fantini Offline

    MHB Craftsman

    Fantini
  6. MarkFL Offline

    Pessimist Singularitarian

    MarkFL
  7. mathmaniac Offline

    MHB Craftsman

    mathmaniac
  8. mente oscura Offline

    MHB Craftsman

    mente oscura
  9. Peter Offline

    MHB Master

    Peter
  10. Petrus Offline

    MHB Journeyman

    Petrus
Showing Friends 1 to 10 of 17
Page 1 of 2 12 LastLast
No results to show...
Ranks Showcase - 1 Ranks
Icon Image Description



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