A Unified Approach to Formal Arakawa-Kaneko Type Zeta Values via Iterated Integrals

Source abstract

We introduce a formal multiple polylogarithm function (FMPF) and general formal Arakawa-Kaneko zeta values (GFAKZVs), and establish several useful properties analogous to those of the ordinary Arakawa-Kaneko zeta values by employing the method of iterated integrals, a powerful tool originating in algebraic topology. In particular, we prove various duality and sum formulas involving FMPFs and GFAKZVs. This allows us to derive, in a uniform manner, a number of known results concerning Arakawa-Kaneko zeta values and Kaneko-Tsumura $ψ$-values that were previously obtained by different approaches, thereby highlighting the unifying power of the iterated integral formalism.