On how n and i turned out to become indices in mathematical sequences and formulae |
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| Authors: | Gert Schubring |
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| Institution: | 1. Fakult?t f??r Mathematik, Universit?t Bietefeld, Postfach 100 131, 33501, Bielefeld, Germany
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| Abstract: | The evolution of indexing sequences and series has been little studied so far, although this topic presents difficulties for students. This symbolisation signified, however, an important means for operating more generally with finite and infinite series. This paper investigates the first steps during the eighteenth century and then the different processes in France and in Germany. In France, it was Lacroix with his textbooks from the end of the eighteenth and the early nineteenth century who paved the way, while dealing with difference series, for what would be established by Cauchy as a general practice with indexed sequences. In Germany, a pivotal role was played by the combinatorial school since the 1780s in establishing sophisticated indexing notations; the achievements by Dirksen in elaborating ??higher-order?? indexing notations prove to be decisive. |
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