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==Mathematics== * [[Peter Gustav Lejeune Dirichlet]] publishes a memoir giving the [[Dirichlet conditions]], showing for which functions the convergence of the [[Fourier series]] holds; introducing [[Dirichlet's test]] for the convergence of series; the [[Dirichlet function]] as an example that not any function is integrable; and, in the proof of the theorem for the Fourier series, the [[Dirichlet kernel]] and [[Dirichlet integral]].<ref>{{cite book|last=Bressoud|first=David M.|title=A radical approach to real analysis|edition=2nd|year=2007|publisher=Mathematical Association of America|location=[Washington, D.C.]|isbn=978-0-88385-747-2|pages=218–227}}</ref> He also introduces a general modern concept for a [[Function (mathematics)|function]].<ref>{{cite journal|last=Elstrodt|first=Jürgen|journal=Clay Mathematics Proceedings|title=The Life and Work of Gustav Lejeune Dirichlet (1805–1859)|volume=7|year=2007|url=http://www.uni-math.gwdg.de/tschinkel/gauss-dirichlet/elstrodt-new.pdf|accessdate=2011-10-20|archive-date=2021-05-22|archive-url=https://web.archive.org/web/20210522140235/http://www.uni-math.gwdg.de/tschinkel/gauss-dirichlet/elstrodt-new.pdf|url-status=dead}}</ref> * [[Nikolai Ivanovich Lobachevsky]] publishes his work on hyperbolic [[non-Euclidean geometry]].<ref>{{cite book|pages=108–111|first=Tony|last=Crilly|title=50 Mathematical Ideas you really need to know|location=London|publisher=Quercus|year=2007|isbn=978-1-84724-008-8}}</ref> * [[Siméon Denis Poisson|S. D. Poisson]] publishes ''Sur l'attraction des sphéroides''.
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