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.^[1]

Leopold Gegenbauer was the son of a doctor. He studied at the

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

Gegenbauer also gave his name to arithmetic functions studied in analytic number theory. The Gegenbauer functions Ρ and ρ (upper case and lower case rho) are defined as follows.^[2]

${\displaystyle P_{a,r}(n):=\sum _{d\,\mid \,n;d^{1/r}\in \mathbb {N} }d^{a}=:n^{a}\rho _{-a,r}(n)}$

In 1973 in Vienna in the district of Floridsdorf (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

References