Document Type


Publication Date



In this paper we investigate two problems concerning the theory of power series in 18th-century mathematics: the development of a given function into a power series and the inverse problem, the return from a given power series to the function of which this power series is the development. The way of conceiving and solving these problems closely depended on the notion of function and in particular on the conception of a series as the result of a formal transformation of a function. After describing the procedures considered acceptable by 18th-century mathematicians, we examine in detail the different strategies—both direct and inverse, that is, synthetic and analytical—they employed to solve these problems.


NOTICE: this is the author’s version of a work that was accepted for publication in Historia Mathematica. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Historia Mathematica, volume 30, issue 1, in 2003.

The Creative Commons license below applies only to this version of the article.

Peer Reviewed




Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.