Nerlund, Nils Eric

Born in the city of Slagelse (northern Denmark) in the family of a pharmacist. All three children in this family became famous - the younger sister Margrethe married Niels Bohr in 1912, and the younger brother Pole became a famous archaeologist and director of the National Museum in Copenhagen. In 1903, Niels Nörlund entered the University of Copenhagen , where he enthusiastically studied mathematics and astronomy. In 1905, Norlund published his first article, where he argued that one of the double stars in the constellation Ursa Major is actually triple . This excellent theoretical and observational work was highly appreciated by Thorvald Thiele , who took Nerlund as an assistant at the Astronomical Observatory of the University of Copenhagen. During his student years, Nerlund also published several serious mathematical works on continued fractions and difference equations ^[7] ,

In 1910, Nörlund graduated from the university and defended his thesis. In 1912, he married Agnete Waever ; they had two daughters ^[7] . For the next 10 years, Nörlund taught mathematics at Lund University (Sweden). In 1916, his work on differential equations received the Grand Prix des sciences mathématiques of the Paris Academy of Sciences and the Gold Medal of the Royal Institution of London. Since 1916, he was a longtime editor of the prestigious journal Acta Mathematica ^[8] . In 1920 - guest speaker at the International Congress of Mathematicians in Strasbourg .

In 1922, the University of Copenhagen organized a third department of mathematics especially for Nörlund, and Nörlund returned to Denmark. For more than 30 years (1923-1956) he taught at the University of Copenhagen. In 1933-1934 he was the rector of the university. At the same time, he held several more posts: director of the created on his initiative (1923–1955), head of the Danish Geodetic Service ^[7] , member of the Commission for Scientific Research in Greenland. In 1925 he created seismographic stations in Denmark and Greenland.

In 1924, Nörlund published the monograph Lectures on Differential Calculus ( Vorlesungen über Differenzenrechnung ), the first book that developed difference calculus from the standpoint of the theory of complex functions and included new studies related to the analytical and asymptotic behavior of solutions of linear difference equations .

Part of the works of Nerlund are devoted to Bernoulli polynomials , as well as generalized hypergeometric functions . He studied the factorial series, their transformations, and the interpolation series included in their solutions. He proved that the factorial series converges uniformly on the half-plane and can represent a function in a certain neighborhood of a single point. He showed that linear differential equations , the coefficients of which can be expanded in factorial series, have a fundamental system of solutions, which can be expressed in terms of the factorial series. He proposed the “Nerlund summation method” of ^{[7] [9]} .

• Vorlesungen über Differenzenrechnung. - Berlin: Springer-Verlag, 1924. ^[10]
• Leçons sur les équations linéaires aux différences finies. - Paris: Gauthier-Villars, 1929. ^[11]
• Vermessungsarbeiten in Grönland, Island und Dänemark. - Darmstadt, 1939.
• The logarithmic solutions of the hypergeometric equation // K. Dan. Vidensk. Selsk. Mat. Fys. Skr. : journal. - 1963. - Vol. 5 . - P. 1-58 .

• Norlund-Rice Integral
• Inge Lehmann

• Bogolyubov A.N. Mathematics. The mechanics. Biographical reference . - Kiev: Naukova Dumka, 1983 .-- S. 345 .-- 639 p.

• John J. O'Connor and Edmund F. Robertson . Nörlund, Nils Eric (Eng.) - biography in the MacTutor archive.
• Nerlund, Nils Eric (Eng.) In the project “ Mathematical Genealogy ”