## A Treaty of Symmetric Function Part 1 Sums of Power

**Authors:** Mohd Shukri Abd Shukor

Sum of Power had gathered interest of many classical mathematicians for more than two thousand
years ago. The quests of finding sum of power or discrete sum of numerical power can be traced back
from the time of Archimedes in third BC then to Faulhaber in the sixteen century. Until today there is
no closed form sums of power formulation for an arithmetic progression has been found. Many
mathematicians were involved in this research and many approaches have been introduced but none is
found to be conclusive. The generalized equation for sums of power discovered in this research has
been compared to Faulhaber's sums of power for integers and it is found that this new generalized
equation can be used for both integers and arithmetic progression, thus offering a new frontier in
studying symmetric function, Fermat's last theorem, Riemman's Zeta function etc.

**Comments:** 47 pages

**Download:** **PDF**

### Submission history

[v1] 15 Dec 2010

[v2] 19 Nov 2011

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