#Check work

81 messages · Page 1 of 1 (latest)

junior lynx
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Can someone check to see if I made an error?

IMG_1830.jpg
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Im almost positive I did something wrong

main onyx
# junior lynx Can someone check to see if I made an error?

I am a little confused:

  1. What is the ζ(s) doing in the sum?
  2. What variable are you integrating with respect to? The only variables I see are (k, s, n), both k and n are those of the sum, and if it was s, then the entire sum is independent and can be pulled out, especially since the ζ is independent of the sum
  3. For the anti derivative at the bottom, n≠-1, not 1
  4. Lastly, we usually do not really calculate and use decimal values, we keep things such as ζ(3) (Apèry's constant) or η(3) as they are, since they're considered more-or-less a closed form, using numbers to represent things gets messy, as you can see

From what I understand, you meant ζ(k)? And an empty integral? Just multiplying the difference between Φ and ψ with the value of the sum?

junior lynx
main onyx
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You have defined zeta inside the sum itself, without having any k in it

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$\int_{\psi}^{\phi}\sum_{k=1}^{13}\frac{2\left(\zeta(s)=\sum_{n\ge1}\frac{(-1)^{n+1}}{n^3}\right)}{\sin\left(\frac{\pi}{4}+\frac{k-1}{6}\pi\right)\cdot\sin\left(\frac{\pi}{4}+\frac{k}{6}\pi\right)}$

rich orioleBOT
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Leonhard Paul Euler

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main onyx
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This is the question

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No?

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As per what I see in the paper

junior lynx
main onyx
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Well, there are a few problems

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Firstly, the definition of zeta is wrong

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This is eta

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Secondly, as I mentioned initially, what is the integral with respect to?

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What are you integrating

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Thirdly, there is no "k" in the numerator

junior lynx
main onyx
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Hmmm

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So it is ζ(k)?

junior lynx
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I’m pretty sure it is I just didn’t question it

main onyx
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Well, you see

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,w zeta(1)

rich orioleBOT
main onyx
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You cannot do that

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At k=1, the zeta function is divergent

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And the denominator is a product of two sin functions, the most it can be is 1

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So this sum diverges

junior lynx
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I feel like a total dumbass right now

main onyx
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No worries, I like analysis, I can help

main onyx
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I think it could be eta(k)?

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Since the definition you wrote next to the zeta is that of eta

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But still am unsure what the integral is supposed to be doing

junior lynx
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Again, I’m just rusty but he thinks I can do all of his work for him

main onyx
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It sounds like nonsense to be honest

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Let me rewrite the question

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In the way it would make some sense

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$\int_{\psi}^{\phi}\dd x\sum_{k=1}^{13}\frac{2\eta(k)}{\sin\left(\frac{\pi}{4}+\frac{k-1}{6}\pi\right)\cdot\sin\left(\frac{\pi}{4}+\frac{k}{6}\pi\right)}$

rich orioleBOT
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Leonhard Paul Euler

351385565586915329.png
main onyx
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The integral is just there

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Doing nothing

junior lynx
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So I would only be solving for the summation?

main onyx
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I highly suggest you double check the question with your friends

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Then, I can help you solve it

junior lynx
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Yeah I took calculus courses in college about five years ago and my friend is taking them now so he thinks I can do anything even though I forgot a big majority of it

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I’ll try and solve it now

main onyx
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So he just sent some random nonsense expecting it to mean something?

junior lynx
main onyx
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I see

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It is alright

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We all make mistakes

junior lynx
# main onyx I see

Nowadays, I just do death metal vocals and work at an aquarium science lab and I haven’t looked back at calculus in an extremely long time but I’m thinking about getting back into it

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Any advice?

main onyx
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I highly recommend you start with the basics

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Even if as low level as trigonometry

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There are thousands of courses and YouTube playlists and books on calculus

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Even Coursera has some stuff

junior lynx
main onyx
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Then you should really get refreshed

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I myself am refreshing on some courses

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Calculus included

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It is good to refresh every once in a while

junior lynx
main onyx
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Now I am revising complex analysis

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Did differential equations, calculus, proofs, number theory, real analysis, etc...

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Going over everything

junior lynx
main onyx
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I have multiple jobs, one of which is a researcher

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And one of my areas of research is math

junior lynx
main onyx
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Use Calculus to calculate sizes

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Volumes

junior lynx
main onyx
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Ah

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Well, it is nice to do math on the side

junior lynx
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@main onyx would you say that math skills equate to intelligence? Or is it just something that anyone can do if they study long enough?

main onyx
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Of course some sort of intelligence is required, from the point of, take someone that has brain issues, of course they cannot do complex math, but for the average person, I say with a good enough teacher, and enough time, they can do some advanced math pretty well

junior lynx