I find that multiple sums are a very interesting concept. However, an even more interesting concept for me is the sum of such sums (the sum of multiple sums). The sum of multiple sums can be turned into a simple product by the formula in the first attached image.
What mathematical applications could this formula have? Where could it be useful?
I have found 2 interesting applications:
1- sum of multiple zeta values (see image 2).
2- sum of multiple power sums (see image 3).
Could you suggest any applications for these 2 particular cases? Could you suggest additional particular cases that would be of interest to mathematicians or physicists?
It has lots of applications in data analysis., in particular, mathematical/statistical modelling for scientific computing. Also https://www.techrepublic.com/article/how-to-use-excels-data-model-to-turn-related-data-into-meaningful-information/
Dear Muhammad Ali
Thank you for your recommendation. I have check the link, however, I did not see how the sum of multiple sums could be used in such cases. Could you elaborate please? Can you give me details about how it actually helps in data analysis?
Thank you for your time.
I have used such things by using tensor analysis, hypergeometric functions, exponential families of distributions, via ultimate use of saddle point approximation, with significant use such sums. Also it ha significant use in numerical partial differential equations. It very important and its concepts could be elaborated by understanding tensor analysis with its applications. The main concept of such thing is nothing but further generalizations e.g., functional is a generalization of function, tensor is generalization of vector, manifold is generalization of Euclidean surfaces etc.,... However., the concepts of all such things getting clear with experience and a really need of its applicability.
R 5, posted 2021/02/17
Roudy El Haddad Dear Roudy, you are researching in algebra.
Are you well instructed in the fundamental rules?
Could you name the prove of (-1) (-1) = +1 ?
Did you read Martinez (negative math)?
Dear Peter Kepp
Why are you asking?
Please respond when you read this.
Did I make any mistakes in my preprints ? Is there applications in algebra you want to tell me about?
Dear Roudy El Haddad
It´s not on any mistake. I try to make you interested in new knowledge in algebra.
If one does algebra today one will use the rules of multiplication based on the binomials. But that is no prove! Martinez showed that the alternating rules also work well.
So there was no unambiguous rule until my research. Interested?
I am always interested in learning more mathematics. And to answer your previous question: No I am not well instructed on the rules and do not know the proofs you talk about. My issue is that I live in a country with terrible living conditions (Lebanon) and I did not get the chance to study mathematics in university. However, mathematics is my passion and nothing is going to stop me from acheiving my dream. The 2 articles I have posted are 2 of the articles that I wrote at 17. I have been doing research since age 12.
One day I will become the greatest mathematician ever (or I will die trying 😂).
Sorry to bore you with my story. Currently I am not very well informed on the subject. In general, I work on a subject and I just teach myself the things I need on the way (in the process). However, next year I am going to try and get into a math major.
My main fields are in order of importance:
1- Number Theory
2- Combinatorics / Discrete Mathematics
3- Analysis
Whatever you do in math you will use the rules of expert opinion.
But expert opinion failes!
Algebra gets defined by field. Field is on two groups each by a special rule of combination of the members of the groups ...
Please look at my homepage and get back here for detailed information or help.
www.mathe-neu.de
You may start with my papers here at RG.
Regards, Peter
- Badges
- Science topic
- Similar topics
- Linguistics
- Composition Studies
- Publication