|
Gegenbauer
Gegenbauer is a German surname. Notable people with the surname include: * Josef Anton Gegenbauer (1800–1876), German historical and portrait painter *Leopold Gegenbauer (1849–1903), Austrian mathematician See also *Karl Gegenbaur (1826–1903), German anatomist and professor *Gegenbauer polynomials In mathematics, Gegenbauer polynomials or ultraspherical polynomials ''C''(''x'') are orthogonal polynomials on the interval minus;1,1with respect to the weight function (1 − ''x''2)''α''–1/2. They generalize Legendre polyn ..., in mathematics {{surname, Gegenbauer German-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leopold Gegenbauer
Leopold Bernhard Gegenbauer (2 February 1849, Asperhofen – 3 June 1903, Gießhübl) was an Austrian mathematician remembered best as an algebraist. Gegenbauer polynomials are named after him. Leopold Gegenbauer was the son of a doctor. He studied at the University of Vienna from 1869 until 1873. He then went to Berlin where he studied from 1873 to 1875 working under Weierstrass and Kronecker. After graduating from Berlin, Gegenbauer was appointed to the position of extraordinary professor at the University of Czernowitz in 1875. Czernowitz, on the upper Prut River in the Carpathian foothills, was at that time in the Austrian Empire but after World War I it was in Romania, then after 1944 it became Chernivtsi, Ukraine. Czernowitz University was founded in 1875 and Gegenbauer was the first professor of mathematics there. He remained in Czernowitz for three years before moving to the University of Innsbruck where he worked with Otto Stolz. Again he held the position of ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gegenbauer Polynomials
In mathematics, Gegenbauer polynomials or ultraspherical polynomials ''C''(''x'') are orthogonal polynomials on the interval [−1,1] with respect to the weight function (1 − ''x''2)''α''–1/2. They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials. They are named after Leopold Gegenbauer. Characterizations File:Plot of the Gegenbauer polynomial C n^(m)(x) with n=10 and m=1 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg, Plot of the Gegenbauer polynomial C n^(m)(x) with n=10 and m=1 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D File:Mplwp gegenbauer Cn05a1.svg, Gegenbauer polynomials with ''α''=1 File:Mplwp gegenbauer Cn05a2.svg, Gegenbauer polynomials with ''α''=2 File:Mplwp gegenbauer Cn05a3.svg, Gegenbauer polynomials with ''α''=3 File:Gegenbauer polynomials.gif, An animation showi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Josef Anton Gegenbauer
Josef Anton von Gegenbaur (6 March 1800, in Wangen, Württemberg – 31 January 1876, in Rome) was an accomplished German historical and portrait painter. Biography He studied first at the Royal Academy in Munich under Robert von Langer, remaining in that city from 1815 to 1823. Among his productions there were two idyllic works, a "Saint Sebastian" and a "Madonna and Child", altar-piece for his native town. In 1823 the painter went to Rome, where he remained until 1826, studying especially the works of Raphael. He became successful as a fresco painter, and, on his return to Württemberg, the king made him court painter and commissioned him to decorate the Royal Villa of Schloss Rosenstein. In 1829 Gegenbaur went again to Rome and worked on frescoes. During later residence in Stuttgart Stuttgart (; Swabian: ; ) is the capital and largest city of the German state of Baden-Württemberg. It is located on the Neckar river in a fertile valley known as the ''Stuttgarter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Gegenbaur
Karl Gegenbaur (21 August 1826 – 14 June 1903)"Karl Gegenbaur – Encyclopædia Britannica" (biography), ''Encyclopædia Britannica'', 2006, Britannica.coBritannica-KarlG was a German anatomist and professor who demonstrated that the field of comparative anatomy offers important evidence supporting of the theory of evolution. As a professor of anatomy at the University of Jena (1855–1873) and at the University of Heidelberg (1873–1903), Karl Gegenbaur was a strong supporter of Charles Darwin's theory of organic evolution, having taught and worked, beginning in 1858, with Ernst Haeckel, eight years his junior. Gegenbaur's book ''Grundzüge der vergleichenden Anatomie'' (1859; English translation ''Elements of Comparative Anatomy'' by Francis Jeffrey Bell, 1878) became the standard textbook, at the time, of evolutionary morphology (biology), morphology, emphasizing that structural similarities among various animals provide clues to their evolutionary history. Karl Gegenbaur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
