Recurrence Relations for Linear Euler Harmonic Sums

Source abstract

Euler's pioneering work on linear and non-linear harmonic sums has continued to inspire extensive research, yielding many new results. This paper studies representations of linear harmonic Euler sums of both even and odd weight. This work establishes new identites linking sums with positive terms to alternating series, introduces two symmetry properties at half integer value, and extends known recurrence relations for linear harmonic Euler sums of even and odd weight.