E. H. Dirksen's contributions to the foundation of analysis
Enno Heeren Dirksen (1788--1850) was a full professor of mathematics at Berlin University since 1824 and in several respects a transitionary figure. The author gives information on one little known contribution by Dirksen to introduce rigour into the foundations of analysis. His review (1829) of Cauchy's \textit{Cours d'Analyse} showed a gap in Cauchy's alleged proof that the limit function of a series of continuous functions is continuous. Schubring explains that Dirksen introduced some new notation that made it easier to express double (iterated) limits. He argues that in this Dirksen went even further than Abel who introduced a counterexample to Cauchy's theorem. However, Dirksen was stronger as a critic than as a constructive mathematician and did not introduce uniform convergence.
scientific article; zbMATH DE number 1925619