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The theory of series in the 17th and 18th centuries poses several interesting problems to historians. Indeed, mathematicians of the time derived num- ous results that range from the binomial theorem to the Taylor formula, from the power series expansions of elementary functions to trigonometric series, from Stirling s series to series solution of di?erential equations, from theEuler MaclaurinsummationformulatotheLagrangeinversiontheorem, from Laplace s theory of generating functions to the calculus of operations, etc. Most of these results were, however, derived using methods that would be...

The theory of series in the 17th and 18th centuries poses several interesting problems to historians. Indeed, mathematicians of the time derived num- ous results that range from the binomial theorem to the Taylor formula, from the power series expansions of elementary functions to trigonometric series, from Stirling s series to series solution of di?erential equations, from theEuler MaclaurinsummationformulatotheLagrangeinversiontheorem, from Laplace s theory of generating functions to the calculus of operations, etc. Most of these results were, however, derived using methods that would be...