Euler's troublesome series: An early example of the use of trigonometric series

This paper discusses the role of the series expansion of (1 - g cos ω)-μ in the works of Leonhard Euler. Two of his papers are considered in detail, his 1748 prize-winning essay on Saturn and Jupiter to the Paris Academy, and his 1756 prize-winning essay, also to the Paris Academy, on planetary perturbations. A close examination of these works indicates that Euler was more concerned with convergence issues than he traditionally has been credited with being