Abstract
Although the first use of the term convergence can be attributed to Gregory in 1668, the concept of convergence as we use it today was not defined explicitly until the 19th century. Ever since the invention of the infinitesimal calculus, the use of divergent series had been surrounded by controversy. They were effectively banned at the beginning of the 19th century, but were rehabilitated at the end of the century by introducing the idea of summation. Poincaré played a fundamental role in the theory of summation. In Les méthodes nouvelles de la Mécanique céleste, he explains the different approaches to the meaning of convergence:
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Chabert, JL. (1999). Acceleration of Convergence. In: Chabert, JL. (eds) A History of Algorithms. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18192-4_15
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DOI: https://doi.org/10.1007/978-3-642-18192-4_15
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