Derivative of Riemann Zeta Function

Zeta function is defined to be the series of 1/n^s from n=1 to n=infinity. What fun facts do you know about the Zeta function? Leave it in the comment!

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bprp fast

[MathAdam]

I have a small question about the non-trivial zeros of this function which I'd like you to address....

[ranjitkalita]

As a biology I don't have much knowledge about maths but still love to see u explain stuff

[factorization]

You can start at n=2 because when n=1, ln1 is 0.

[H-pv]

zeta(-1) by hand
*Believe in algebra, not wolframalpha*

[shehnazsalahuddin]

A very cool derivative. And a wonderful way to solve it

[juanpina]

Fantastic, but the left part of the Riemman Zeta function is missing. When Re(z)<1 or is equal to 1

[silvally]

Newton-Raphson Method: Guess, Imma prove the Riemann Hypothesis.

[richypichy-minecraft]

You can change the sum to go from 2 to inf, because ln(1) is 0 anyways...

[adityaekbote]

Next vid proof of Riemann zeta function plus integral for the bonus

[TechnetiumPrime]

He differentiated eulers zeta function, but when real(s)<1 it is undefined and requires analytic continuation (that is the reimann zeta function).

[mrtthepianoman]

But this only works where the Riemann Zeta function corresponds to that sum (Re(s)>1). What about on the rest of it's domain?

[CPNEWZ]

How would you find the series expansion for the derivative?

[avalanche]

He is deriving his power from his Dragon ball.

[maximevanderbeken]

The only hard part is the one he skipped ; showing why you can switch the sum and the d/ds...

[farklegriffen]

I feel like this is wrong, shouldn’t d/dx b^-x = b^-x ln(1/b)?
Because d/dx b^-x = d/dx (b^-1)^x = b^-x ln(b^-1)

[dudono]

Does this derivative work everywhere or just for re(s) > 1?

[kilian]

You didn’t really justify interchanging the sum and the derivative.

[ealejandrochavez]

That formula (and derivation) only works when the real part of s is greater than 1.

[meenadeshpande]

Hi This is Abhijeet Deshpande and....

This is how to understand the theorem....

Points:

1.) From 1 to 100, calculate the number of odds and evens
2.) Now for every single of the odd and even numbers, measure and write down the number of steps, for both to go to the number 4.

3.) For both the odd and even numbers, calculate individually as below,
a.) Add the number of steps to get a total of both odd and even
b.) Get a total of odd / even numbers by addition
i.e.
a.) How many numbers are odd and even
b.) And what the the sum total of odd and even by addition
c.) What is the sum total of odd and even by division
d.) What is the sum total of odd and even numbers by substraction

4.) Divide the number of steps with the number of odd / even numbers wiithin 1 to 100
5.) Now upon fiding the value of the division of both odd and even numbers,

Use the above results of calculations to calculate with the results to determine the base structure or the point of average c
divisions or calculations, where both the calculations of odd and even align,

And Voila, you have a symmetry of calculative set of equations that would determine the results of any similar supposedly unsolvable equations.

These equative calculations of mine can also solve the problems of Rieman hypothesis of prime numbers as well.

As such I am eligible to win the seed of Clay Institute for of and towards the same.

3x+1, Rieman Hypothesis
© Abhijeet Deshpande, 2021

[lasa]

My curiosity took me over again 😥 ohh and calculate the sum🙂