A family of integral representations for the voltammetric responses of reversible electrochemical reactions, arising from Abel, Lindelöf and Euler-Ramanujan summations of the alternating series solution

Abstract

Given the closed-form expression for the mass transfer function M(p) pertaining to one-dimensional mass transport conditions in the electrolyte, the linear-sweep-voltammetry response of reversible electrochemical reactions involving soluble species is derived as an infinite series that is conditionally convergent, depending on the electrode potential imposed. The alternating feature of this series greatly simplifies its summation process, even in its divergence domain, using appropriate nonlinear sequence transformations (NLST) together with the high-precision computing mode of computer algebra systems (CAS). Alternatively, the use of Abel, Lindelöf and Euler-Ramanujan summation formulae enables the Faradaic current to be modelled as three integral representations, which can be evaluated numerically using self-adaptive numerical integration procedures implemented in CAS software. The highly accurate data, either obtained from NLST summation of the infinite series solution, or evaluated numerically from the associated integral representations, could be used as benchmark data for checking the computation accuracy of other numerical methods.