Discovering and Proving Infinite Pochhammer Sum Identities

Understand

We consider nested sums involving the Pochhammer symbol at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi,$ $\log(2)$ or zeta values.

• In order to perform these simplifications, we view the series as specializations of generating series.
• For these generating series, we derive integral representations in terms of root-valued iterated integrals or directly in terms of cyclotomic harmonic polylogarithms.
• Using substitutions, we express the root-valued iterated integrals as cyclotomic harmonic polylogarithms.