Niels Nielsen (2 December 1865, in Ørslev – 16 September 1931, in

Copenhagen Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan ar ...

) was a Danish mathematician who specialised in

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

Life and work

Nielsen was the son of humble peasants and grew up in the western part of the island of

Funen Funen ( da, Fyn, ), with an area of , is the third-largest island of Denmark, after Zealand and Vendsyssel-Thy. It is the 165th-largest island in the world. It is located in the central part of the country and has a population of 469,947 as of ...

. In 1891 he graduated in mathematics from the University of Copenhagen and in 1895 obtained his doctorate. In 1909 he succeeded

Julius Petersen Julius Peter Christian Petersen (16 June 1839, Sorø, West Zealand – 5 August 1910, Copenhagen) was a Danish mathematician. His contributions to the field of mathematics led to the birth of graph theory. Biography Petersen's interests i ...

as Professor of Mathematics at the University of Copenhagen. His most original works were on

special functions Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by ...

, with an important contribution to the theory of the

gamma function In mathematics, the gamma function (represented by , the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except ...

. In 1917 he suffered from an illness from which he never fully recovered. From this date onward he became interested in the

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

Bernoulli numbers In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in analysis. The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, ...

Stirling numbers In mathematics, Stirling numbers arise in a variety of analytic and combinatorial problems. They are named after James Stirling, who introduced them in a purely algebraic setting in his book ''Methodus differentialis'' (1730). They were rediscove ...

, and the

history of mathematics The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments ...

, writing two books on Danish mathematicians of the time period 1528-1908, and two other books on French mathematicians.

Selected publications

* ''Om en klasse bestemte integraler og nogle derved definerede semi-periodiske funktioner'', J. Møller, 1895 (dänisch; Dissertation) * ''Handbuch der Theorie der Cylinderfunktionen'', B. G. Teubner, Leipzig 1904
im Internet-Archiv
* ''Handbuch der Theorie der Gammafunktion'', B. G. Teubner, Leipzig 1906
im Internet-Archivditodito
* ''Theorie des Integrallogarithmus und verwandter Transzendenten'', B. G. Teubner, Leipzig 1906
im Internet-Archivbei der Cornell University
* ''Der Eulersche Dilogarithmus und seine Verallgemeinerungen'', E. Karras, 1909; Nova Acta Leopoldina 90, 1909, S. 121–212

* ''Lehrbuch der unendlichen Reihen. Vorlesungen gehalten an der Universität Kopenhagen'', B. G. Teubner, Leipzig 1909
im Internet-Archivbei der Cornell University
* ''Matematiken i Danmark. Bidrag til en bibliografisk-historisk oversigt'' (Mathematik in Dänemark. Beiträge zu einem bibliographisch-historischen Überblick), 2 Bände ''1801–1908'' und ''1528–1800'', Gyldendalske Boghandel Nordisk Forlag, København & Kristiania 1910 1912 (dänisch) * ''Elemente der Funktionentheorie. Vorlesungen gehalten an der Universität Kopenhagen'', B. G. Teubner, Leipzig 1911
bei der Cornell University
* ''Traité élémentaire des nombres de Bernoulli'', Gauthier-Villars, Paris 1923 (französisch
bei Gallica
* ''Franske matematikere under revolutionen'', Bianco Lunos Bogtrykkeri, 1927 (dänisch; mit 76 Mathematiker-Biographien); ''Géomètres français sous la révolution'', Levin & Munksgaard, 1929 (französische Übersetzung

References

Harald Bohr Harald August Bohr (22 April 1887 – 22 January 1951) was a Danish mathematician and footballer. After receiving his doctorate in 1910, Bohr became an eminent mathematician, founding the field of almost periodic functions. His brother was the No ...

: ''Niels Nielsen 2. December 1865 – 16. September 1931'', Matematisk Tidsskrift B, 1931, S. 41–45. * Thøger Bang: ''Niels Nielsen 1865–1931'', Nordisk Matematisk Tidsskrift 13, 1965, S. 121–122.

External links

* *
Niels Nielsen on Theseus
{{DEFAULTSORT:Nielsen, Niels 1865 births 1931 deaths 19th-century Danish mathematicians 20th-century Danish mathematicians Mathematical analysts University of Copenhagen alumni University of Copenhagen faculty Danish historians of mathematics People from Vordingborg Municipality