On sums of powers in Ramanujan's lost notebook

Abstract

On one page in his lost notebook, Ramanujan records seven formulas for sums of powers. The meaning of these formulas is not clear. We provide a proper interpretation and indicate their connection with maximum and minimum values of Bernoulli polynomials.

Keywords:

• sums of powers
• Ramanujan's lost notebook
• Bernoulli polynomials

AMS Subject Classification::

• 11B68