Summation to product, to summation

[half cape]

I feel like I am missing quite a bit here in my process. I tried to model from the basel problem, but I don't think I did this correctly.

[thorn cypress]

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[verbal shale]

in the expansion what is x?

what are you even doing here

[half cape]

I'm doing stuff.

Nah

I'm just justing to solve for zeta3 using a simliar method of how euler solved zeta2

No big deal

There's some things I'm just not knowledgeable in

x = square root 1/n^3

Which are the roots of that particular sin function

[half cape]

Question is, what are we all even doing here.

One mistake I did make was writing the numerators incorrectly in the product series.

There're all supposed to be x^2

[verbal shale]

i meant it in the context of the problem

there's no motivation behind anything

[half cape]

What are you, a ballet instructor?

What do you mean there's no motivation Coffee

[verbal shale]

In context of a mathematical proof, motivation means why we do something or the reason behind doing something

[half cape]

Ah, it's to solve for zeta(3)

very basic

[verbal shale]

the 3rd line pops out of nowhere kinda

[half cape]

OHHH

You mean the logical leaps being made without any context

[verbal shale]

yes

[half cape]

So, factored out x in the taylor series, so that all the x terms had exponents 2n

[verbal shale]

why is x in the last sum equation

[half cape]

Why is x there?

[verbal shale]

yes

[half cape]

Have you ever read anything about the basel problem?

[verbal shale]

yes

there's a proof where they use a similar tactic

Not sure its directly applicable here though

[half cape]

I'm not sure either

[verbal shale]

but still what's x in the last line?

[half cape]

That's why I need help

[verbal shale]

this isn't understandable

[half cape]

x^2 is some coefficient that equates to n=2 in the taylor series

That's been expanded out of the weierstrass product series

[verbal shale]

Where's the x in the middle expression on the first like and forget the exponent of cbrt x as 2n shouldn't you be dividing by cbrt x?

[half cape]

Good point....

I think...

No, cause then I wouldn't be able to find the number for x^2 in the taylor series

[verbal shale]

why do you want to find that

[half cape]

Find zeta(3)?

or the x^2

[verbal shale]

write a full proof with reasoning and you'll see where you break logic yourself

[half cape]

I don't know how to write a proof

[verbal shale]

it's faster than writing down 3 lines and trying to find out the error

[half cape]

Or how to use reasoning.

[verbal shale]

just ask yourself "why is this true"

and write it down

[half cape]

Sounds like a plan

Stan

[verbal shale]

yes very good plan

[half cape]

My dear math majoring coffee

Has math broke your spirit yet?

[verbal shale]

no

I'm yet to join an uni so not in a strict course rn

[half cape]

Taking a break?

[verbal shale]

no I'm in school

[verbal shale]

anyways let me know when you do this

If I remember zeta(even) has an explicit formula but zeta(odd) is a hassle to derive

[half cape]

Yes, I need a closed form for zeta(3)

[verbal shale]

oh yeah i remember

there's none

[half cape]

So I'll write some stuff done

[verbal shale]

if you find one you'll be one of the greatest mathematicians of the 20 th century

[half cape]

I'm not even a mathematician though

Yet, I've been working on this problem for the last 10 days nonstop

No sleep, no food, no relationships, nothing but zeta(3)

I feel like a crackhead

[verbal shale]

damn

[half cape]

Is this what math is supposed to be like?

[verbal shale]

in short, Noone has a closed form yet

yes

if you are a math graduate working towards finding the closed form

are you?

[half cape]

Nope, this is just a hobby

[verbal shale]

what have you tried in the 10 days?

[half cape]

I tried relating zeta(3) to the liebnitz series for pi

I tried relating it to log2

[verbal shale]

note : when working on unsolved problems, be upto date with the things people already tried

[half cape]

Now I'm trying to relate it using eulers method.

[verbal shale]

that constitutes of reading every research paper on zeta(3)

[half cape]

GOOD ADVICE

[verbal shale]

and also read the whole wiki

then you have a lot more ground to work off of

[half cape]

I don't understand half of what people are talking about. They're using integrals (I haven't even taken calculus) identities I've never heard of making leaps in logic that exponentially difficult to grasp

My thought is this, if everyone's doing the way they're doing and it isn't working, then maybe something different is what the world needs

In otherwords, a dumbass

Maybe they're all too smart for their own good

[verbal shale]

everyone's trying to gnaw at it in some way

but you should know what they did absolutely

you may reproduce their work too by chance

[half cape]

True

But there can only be one winner

[verbal shale]

@half cape you should learn the basics first before going into the open problems

atleast know everything from a Bsc course in pure mathematics

[half cape]

I'm learning as I'm going. Also, I'm still in college. So I'll learn it all anyway.

There's courses on pure math?

I haven't seen any yet

[half cape]

+close