The key word that states the difference between the reasoning that you have written and what I'm doing in Python is "restricted to the main branch". What I'm doing in Python is not restricted to the main branch.
In fact, applying my Python code to the case above stated (sqrt(z+sqrt(z))), we...
Hi all. I tried also today with the algebraic function sqrt(z+sqrt(z)) and it is still working.
1) i tried first the case in which the approximation is developed around 1. It approximated perfectly but it did not generated any fractional exponent (only taylor like terms). Perhaps it is because I...
Sorry it has some extra lines that I wrote to check if the code works. If I find time I will upload again the code without the spurious lines. At least, in UPPERCASE, I commented the important lines:
# -*- coding: utf-8 -*-
"""
Created on Wed Aug 3 16:56:17 2022
@author: thepulp
"""...
Hi all.
While I was waiting for more replies, I developed a Python code in order to check if my intuition works and, surprisingly... IT DOES!
At least for a particular function (sqrt(4-z^2)), this method offers an approximation for both branches of the function. In the following post I will...
Thanks Martinbn for your answer. Just for you to know my background, I have read a couple of complex analysis books with a bit of Riemann Surfaces in them, but I have not read anything fully focused on Riemann Surfaces. In addition I have seen tons of youtube videos and lessons regarding complex...
Yes, you are right, I should have written everything with the same variable "z" and clarifying that I'm talking about a function y(z) of a complex variable z. This function is the solution of this equation:
p1(z)*y(z)n + p2(z)*y(z)n-1 + ... + pn+1(z)*y(z)0 = 0
And I want to write and...
Hi, I'm writting because I sort of had an idea that looks that it should work but, I did not find any paper talking about it. I was thinking about approximating something like algebraic functions. That is to say, a function of a complex variable z,(probably multivalued) that obeys something...
It came to my attention yesterday this, from my ignorant point of view, amazing paper that describes what it looks as another Theory of Everything: https://arxiv.org/abs/2110.02062
If I didnt understand incorrectly, from first principles / a pre quantum theory (Trace Dynamics, 8D octonionic...
Close! My question would be: is analytic continuation of the sum of g(n;-1) equal to the analytic continuation of the sum of f(n;-1)? (given that g(n;-1)=n)
Thanks!
Perhaps this question is not clear. I am trying to ask about other functions that could be used in order to perform the "analytic continuation trick" for the same serie and that may produce a result different than -1/12.
Sorry, this example is for the sum of n*(-1)^n. I was asking for the sum of n.
I don't know if you haven't read my question properly or i have not understood the connection between your example and my question.
Thanks all the same for your answer and in advance for any other answer you may give me.
Hi, I've seen several videos and documents that state that "the sum of all natural numbers is equal to -1/12". The "proof" in general is using ramanjuan summation and analytic continuation of the riemann function.
In this proof, the election of the riemann function in order to perform the...
What does it mean that a sequence is Stable? What I've read is that a method can be stable or not. But not a sequence. I guess, what you are saying is that a pair sequence-method is stable, but I'm not sure.
I'm having trouble understanding you, do you have a reference in order to look at it...
Thank for your answer, but I think we are using different definitions regarding stability. In fact, you say
But the definition of stability is (at least from what I read):
Y(a1;a2;a3;a4;...)=a1+Y(a2;a3;a4;...)
So, If the Zeta Function Sum method "forbids" taking the first term out, then it...
The paper I referenced says that there is an issue with Zeta sum. In fact:
"... In Nesterenko & Pirozhenko (1997) we encounter an attempt to justify the use of the Riemann’s Zeta function. The authors refer to Hardy’s book for the actual method. They use axioms A and B and the zeta function to...