If you are interested in the generalization of Faulhaber’s formula, check my articles “Recurrent Sums and Partition Identities” and “Multiple Sums and Partition Identities”.

You can check them out on my profile.

The first article contains a formula for the recurrent sum of powers.

The second article contains a formula for the multiple sun of powers.

Dear George Stoica

This is true. Pure mathematics is always waiting for applications. Also pure mathematicians like myself are always waiting to see where our contributions are being used inside and outside of mathematics.

It is a mathematician’s greatest trophies to see his/her work being used by others and contributing to the world.

If you ever discover of any applications of Faulhaber’s formula and more importantly of the formula generalized to multiple sums of powers, please let me know.

Thank you.

Dear Ganie Abdul Hamid

In my last 2 articles, I have presented a generalization of Faulhaber’s to multiple sums of powers and to recurrent sums of powers.

For this reason, I am interested in the applications of Faulhaber’s formula. In order to find a practical aspect for my work.

I am not looking for a generalization of Faulhaber’s formula. I am looking for applications. I also have read the paper that you have recommended but it is not really what I am looking for.

Thank you for your time.

Dear Roudy El Haddad,

Please see my paper (and related references) available at https://www.researchgate.net/publication/233720636_A_congruence_modulo_n3_involving_two_consecutive_sums_of_powers_and_its_applications

Preprint Novel Results on Series of Floor and Ceiling Functions

Roudy El Haddad You may see the following article by one of my colleagues, you will notice how Faulhaber's formula is playing a vital role in modern number theory.

I've finally developed a general method just working onto the Telescoping Sum:

Preprint Additive Algebra and new definition of what a Radical is, le...

Preprint Maruelli-The-Two-Hand-Clock-Vol.1-Rev2022-07