Leopold Gegenbauer
Encyclopedia
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 Chernovtsy, 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 extraordinary professor in Innsbruck.
After three years teaching in Innsbruck Gegenbauer was appointed full professor in 1881, then he was appointed full professor at the University of Vienna in 1893. During the session 1897–98 he was Dean of the university. He remained at Vienna until his death. Among the students who studied with him at Vienna were the Slovenian Josip Plemelj
, the American James Pierpont
, Ernst Fischer
, and Lothar von Rechtenstamm.
Gegenbauer had many mathematical interests such as number theory, function theory, and the theory of integration, but he was chiefly an algebraist. He is remembered for the Gegenbauer polynomials
, a class of orthogonal polynomials. They are obtained from the hypergeometric series in certain cases where the series is in fact finite. The Gegenbauer polynomials are solutions to the Gegenbauer differential equation and are generalizations of the associated Legendre polynomials.
In 1973 in Vienna in the district of Floridsdorf
(21. Bezirk) a street was named in his honor the Gegenbauerweg.
Asperhofen
Asperhofen is a town in the district of Sankt Pölten-Land in the Austrian state of Lower Austria....
– 3 June 1903, Gießhübl
Gießhübl
Gießhübl is a town in the district of Mödling in the Austrian state of Lower Austria. It is located in the south of Vienna, the Austrian capital, neighboring the nature protection area Föhrenberge. With an altitude of 416 m, Gießhübl is the highest-located wine-growing district in Lower Austria....
) was an Austrian
Austrians
Austrians are a nation and ethnic group, consisting of the population of the Republic of Austria and its historical predecessor states who share a common Austrian culture and Austrian descent....
mathematician remembered best as an algebraist. Gegenbauer polynomials
Gegenbauer polynomials
In mathematics, Gegenbauer polynomials or ultraspherical polynomials C are orthogonal polynomials on the interval [−1,1] with respect to the weight function α–1/2. They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials...
are named after him.
Leopold Gegenbauer was the son of a doctor. He studied at the University of Vienna
University of Vienna
The University of Vienna is a public university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world...
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
Austrian Empire
The Austrian Empire was a modern era successor empire, which was centered on what is today's Austria and which officially lasted from 1804 to 1867. It was followed by the Empire of Austria-Hungary, whose proclamation was a diplomatic move that elevated Hungary's status within the Austrian Empire...
but after World War I it was in Romania, then after 1944 it became Chernovtsy, 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
Otto Stolz
Otto Stolz was an Austrian mathematician noted for his work on mathematical analysis and infinitesimals. Born in Hall in Tirol, he studied in Innsbruck from 1860 and in Vienna from 1863, receiving his habilitation there in 1867...
. Again he held the position of extraordinary professor in Innsbruck.
After three years teaching in Innsbruck Gegenbauer was appointed full professor in 1881, then he was appointed full professor at the University of Vienna in 1893. During the session 1897–98 he was Dean of the university. He remained at Vienna until his death. Among the students who studied with him at Vienna were the Slovenian Josip Plemelj
Josip Plemelj
Josip Plemelj was a Slovene mathematician, whose main contributions were to the theory of analytic functions and the application of integral equations to potential theory.- Life :...
, the American James Pierpont
James Pierpont (mathematician)
James P. Pierpont was a Connecticut-born American mathematician. His father Cornelius Pierpont was a wealthy New Haven businessman. He did undergraduate studies at Worcester Polytechnic Institute, initially in mechanical engineering, but turned to mathematics. He went to Europe after graduating in...
, Ernst Fischer
Ernst Sigismund Fischer
Ernst Sigismund Fischer was a mathematician born in Vienna, Austria. He worked alongside both Mertens and Minkowski at the Universities of Vienna and Zurich, respectively...
, and Lothar von Rechtenstamm.
Gegenbauer had many mathematical interests such as number theory, function theory, and the theory of integration, but he was chiefly an algebraist. He is remembered for the Gegenbauer polynomials
Gegenbauer polynomials
In mathematics, Gegenbauer polynomials or ultraspherical polynomials C are orthogonal polynomials on the interval [−1,1] with respect to the weight function α–1/2. They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials...
, a class of orthogonal polynomials. They are obtained from the hypergeometric series in certain cases where the series is in fact finite. The Gegenbauer polynomials are solutions to the Gegenbauer differential equation and are generalizations of the associated Legendre polynomials.
In 1973 in Vienna in the district of Floridsdorf
Floridsdorf
Floridsdorf is the 21st district of Vienna, Austria .Floridsdorf is located in the northern part of Vienna.The District Office and the centre of Floridsdorf are located round Am Spitz, at the junction of Prager Straße and Brünner Straße .Since 2004, Floridsdorf has had its own tower: the...
(21. Bezirk) a street was named in his honor the Gegenbauerweg.
Selected works
- Einige Sätze über Determinanten hohen Ranges, 1890
- Über den größten gemeinsamen Theiler, 1892