A treaty of symmetric function: An approach in deriving general formulation for sums of power for an arbitrary arithmetic progression Part 1

Abstract

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 centuries. 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.

Scope:

• Pure Mathematics

Keywords:

• Sums of Power
• Faulhaber’ sums of power
• Symmetric function
• Sums of Numerical Power
• Power Sum