caa a22 4500 445882247 CHVBK 20180317145547.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s10649-010-9286-x doi (NATIONALLICENCE)springer-10.1007/s10649-010-9286-x Schubring Gert Fakultät für Mathematik, Universität Bietefeld, Postfach 100 131, 33501, Bielefeld, Germany aut On how n and i turned out to become indices in mathematical sequences and formulae [Elektronische Daten] [Gert Schubring] 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. Springer Science+Business Media B.V., 2011 Generalisation nationallicence Algebraisation nationallicence Emergence of symbolisation nationallicence Index notation nationallicence Learner difficulties nationallicence Lacroix nationallicence Hindenburg nationallicence Dirksen nationallicence Educational Studies in Mathematics Springer Netherlands 77/2-3(2011-07-01), 331-350 0013-1954 77:2-3<331 2011 77 10649 https://doi.org/10.1007/s10649-010-9286-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10649-010-9286-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Schubring Gert Fakultät für Mathematik, Universität Bietefeld, Postfach 100 131, 33501, Bielefeld, Germany aut NATIONALLICENCE 773 0- Educational Studies in Mathematics Springer Netherlands 77/2-3(2011-07-01), 331-350 0013-1954 77:2-3<331 2011 77 10649 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer