The interest in analytic functions increased toward the end of the XIX century. The explorations of the domain of convergence were conducted using increasingly generalized models of infinite sums: the initial Taylor series was followed by the generic power form and, in turn, the series of polynomials, until analysts detached sequences from specific formulas, so that abstract notations, such as φn(z), referred to functions endowed with selected properties, especially analyticity. In 1899, Giulio Vivanti remarked that analysis was ‘the immediate extension of the theory of infinite series’ [574, p. 263].