• Today, 00:39
Thanks GJA ... your post is extremely helpful and clarifying ... Just a simple point of clarification ... You write: " ... ... Take...
3 replies | 45 view(s)
• Yesterday, 18:19
Eileen has one leg shorter than the other. Is it ok to park where a sign says "Fine for parking"?
59 replies | 9730 view(s)
• Yesterday, 05:54
MarkFL replied to a thread Evolution Self-Destructs in Chat Room
Haha...you went straight for the big gun..."Darwin's Bulldog" himself.
10 replies | 134 view(s)
• Yesterday, 04:27
I just thought I would share with MHB members Duistermaat and Kolk "Remark on notation". This remark occurs after the definition of directional and...
3 replies | 45 view(s)
• Yesterday, 00:56
If we integrate, we get: \ln|f(x)|=C-x This implies: f(x)=\pm e^{C-x}=\pm e^Ce^{-x} Now, let c_1=\pm e^{C} and also let $c_1=0$...
7 replies | 95 view(s)
• Yesterday, 00:34
You haven't studied integration yet?
7 replies | 95 view(s)
• Yesterday, 00:15
Let's use the notation of Leibniz and write: \d{f}{x}=-f(x) Now what if we separate variables and write: \frac{1}{f(x)}\,df=-dx We have...
7 replies | 95 view(s)
• February 22nd, 2018, 23:41
Hello, and welcome to MHB! (Wave) Do you mean: f(x)=-f'(x) ?
7 replies | 95 view(s)
• February 22nd, 2018, 23:30
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 | 45 view(s)
• February 22nd, 2018, 23:01
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 | 27 view(s)
• February 22nd, 2018, 22:24
MarkFL replied to a thread Evolution Self-Destructs in Chat Room
According to what I could find online, Dr. Morris is a young Earth creationist with a degree in geological engineering. If you can point to the peer...
10 replies | 134 view(s)
• February 22nd, 2018, 22:14
MarkFL replied to a thread Evolution Self-Destructs in Chat Room
This argument sounds very similar to: Watchmaker analogy The above article contains some noteworthy criticisms of the analogy. :)
10 replies | 134 view(s)
• February 22nd, 2018, 15:25
It's a "rite of passage" for calculus students. (Smile)
3 replies | 55 view(s)
• February 22nd, 2018, 07:20
l will now attempt to, explicitly, complete the demonstration that Df(a) v = \sum_{ 1 \le j \le n } v_j D_j f(a) \ \ \ \ (v \in \mathbb{R}^n ) ...
4 replies | 77 view(s)
• February 22nd, 2018, 01:11
Here is an attempt to show Df(a) v = \sum_{ 1 \le j \le n } v_j D_j f(a) \ \ \ \ (v \in \mathbb{R}^n ) Now we have ... Df(a) v =...
4 replies | 77 view(s)
• February 22nd, 2018, 00:59
Thanks Country Boy ... ... appreciate the help ... Peter
4 replies | 77 view(s)
• February 22nd, 2018, 00:54
Thanks GJA ... that was really helpful ... Still reflecting on what you have said ... Thanks again ... Peter
2 replies | 63 view(s)
• February 21st, 2018, 23:26
Here is this week's POTW: Let $ABCD$ be a convex quadrilateral with $\overline{AB}=\overline{AD}$. Let $T$ be a point on the diagonal...
0 replies | 49 view(s)
• February 21st, 2018, 23:21
No one answered this weeks POTW...my solution follows: (a) Apply conservation of angular momentum (subscripts of $R$ pertain to the rod, while...
2 replies | 162 view(s)
• February 21st, 2018, 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:...
4 replies | 77 view(s)
• February 21st, 2018, 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:...
1 replies | 42 view(s)
• February 21st, 2018, 00:31
\frac{5}{4}\cdot\frac{4}{3}=\frac{5}{3} :)
14 replies | 236 view(s)
• February 20th, 2018, 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...
• February 20th, 2018, 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 | 82 view(s)
• February 20th, 2018, 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 | 27 view(s)
• February 20th, 2018, 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:...
2 replies | 63 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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