• Today, 07:38
I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2:...
1 replies | 30 view(s)
• Today, 06:50
I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2:...
0 replies | 20 view(s)
• Today, 00:31
\frac{5}{4}\cdot\frac{4}{3}=\frac{5}{3} :)
14 replies | 212 view(s)
• Yesterday, 23:10
MarkFL posted a visitor message on Peter's profile
Sometimes editing a thread title is an issue, but the issue is with vBulletin. If you ever want to change a thread title, and can't, just let me know...
• Yesterday, 22:24
Thanks again Krylov .... BUT ... just a comment on D&K's proof .... I have to say that D&K's proof of Hadamard's Lemma though valid, is not...
3 replies | 72 view(s)
• Yesterday, 21:57
I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2:...
0 replies | 22 view(s)
• Yesterday, 21:26
I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2:...
1 replies | 44 view(s)
• Yesterday, 20:41
Thanks Krylov, ... followed your advice and obtained the result ... Thanks again ... Peter
3 replies | 72 view(s)
• Yesterday, 17:09
I'm going to walk through this problem, using your substitution...let's begin with: I=\int_{0}^{\Large\frac{3\pi}{4}}\int_{0}^{\pi}\int_{0}^{1}...
14 replies | 212 view(s)
• Yesterday, 16:30
Where did the $\cos(\theta)$ come from?
14 replies | 212 view(s)
• Yesterday, 16:28
I was simply taught that a linear function has no concavity...just recalling from memory. :)
20 replies | 238 view(s)
• Yesterday, 16:24
Let's look at an example that more clearly demonstrates the statement regarding concavity isn't always true. Consider: H(x)=\ln(x+1) And so: ...
20 replies | 238 view(s)
• Yesterday, 15:58
Perhaps there are differences in terminology...I was taught that a function is concave up on an interval when its second derivative is positive, and...
20 replies | 238 view(s)
• Yesterday, 15:47
Indeed, and is why I resorted to looking for a function satisfying the given criteria, that is not concave up on the given interval. :)
20 replies | 238 view(s)
• Yesterday, 15:41
You want to reverse the limits of integration, because of the negative sign in the differential resulting from your $u$-substitution (I don't know...
14 replies | 212 view(s)
• Yesterday, 14:37
Suppose $h(t)=c$, where $0<c$...what is $H(x)$?
20 replies | 238 view(s)
• Yesterday, 07:17
Oh! OK ... get the idea ... Thanks ... Peter
2 replies | 56 view(s)
• Yesterday, 07:04
I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2:...
3 replies | 72 view(s)
• Yesterday, 00:23
I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2:...
2 replies | 56 view(s)
• February 19th, 2018, 22:26
I now understand the above limit ... thanks to Ackbach and Krylov ... Thanks to you both ... Peter
3 replies | 76 view(s)
• February 19th, 2018, 22:10
MarkFL replied to a thread 8.7 Two ice skaters in Physics
There were a bunch of COLOR and FONT tags all over the place that I got rid of. :)
6 replies | 87 view(s)
• February 19th, 2018, 22:04
MarkFL replied to a thread 8.7 Two ice skaters in Physics
This is what I see: My bigger concern though is all the extraneous formatting codes, some of which were embedding inside your $\LaTeX$. I do...
6 replies | 87 view(s)
• February 19th, 2018, 20:34
If: u=\cos(\phi) then: du=-\sin(\phi)\,d\phi which would result in reversing the limits of integration. :)
14 replies | 212 view(s)
• February 19th, 2018, 20:14
MarkFL replied to a thread 8.7 Two ice skaters in Physics
As you can see, I've edited your post to remove a whole slew of extraneous formatting BBCodes...if you're going to paste your text from some other...
6 replies | 87 view(s)
• February 19th, 2018, 06:47
3 replies | 71 view(s)
• February 19th, 2018, 06:42
Thanks Krylov ... most clear and helpful ... Thanks again ... Peter
3 replies | 71 view(s)
• February 19th, 2018, 06:23
I am reading the book "Several Real Variables" by Shmuel Kantorovitz ... ... I am currently focused on Chapter 2: Derivation ... ... I need...
3 replies | 71 view(s)
More Activity

### 72 Visitor Messages

1. Hey Balarka, according the the settings in the ACP it is 5 minutes.
2. Hey Balarka, Daniel is upgrading the forum software to a completely new platform. It should be back up soon.
3. I agree that fun shouldn't introduce wrong concepts.

PS: Yes, I'll add one when I start the next post.
4. 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.
5. What is your definition of Regularization ?
6. 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.
7. Hey Balarka , the idea of regularization is giving a finite value for divergent series or integrals. Consider the following
$$\zeta(-2)= 0$$
$$1+4+9+\cdots = 0$$
8. Okay, thanks. I think the former one is just what I wanted.
9. 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.
10. 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.
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#### Basic Information

Date of Birth
January 12, 2000 (18)
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

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