Lazarus Immanuel Fuchs (1833–1902)
5 May 1833|
|Died||26 April 1902
Berlin, German Empire
|Institutions||University of Greifswald
University of Heidelberg
University of Berlin
University of Göttingen
|Alma mater||University of Berlin|
|Doctoral advisor||Karl Weierstraß|
|Doctoral students||Gerhard Hessenberg
|Known for||Fuchsian groups
|Influenced||Jules Henri Poincaré
Marie Ennemond Camille Jordan
Felix Christian Klein
Lazarus Immanuel Fuchs (5 May 1833 – 26 April 1902) was a German mathematician who contributed important research in the field of linear differential equations. He was born in Moschin (Mosina) (located in Grand Duchy of Posen) and died in Berlin, Germany. He was buried in Schöneberg in the St. Matthew's Cemetery. His grave in section H is preserved and listed as a grave of honour of the State of Berlin.
is called Fuchsian if p and q are meromorphic at the point a, and have poles of orders at most 1 and 2, respectively. According to a theorem of Fuchs, this condition is necessary and sufficient for the regularity of the singular point, that is to the existence of two linearly independent solutions of the form
where the exponents can be determined from the equation. In the case when is an integer this formula has to be modified.
Another well-known result of Fuchs is the Fuchs's conditions, the necessary and sufficient conditions for the non-linear differential equation of the form
to be free of movable singularities.
Lasarus Fuchs was the father of Richard Fuchs, a German mathematician.
- Über Funktionen zweier Variabeln, welche durch Umkehrung der Integrale zweier gegebener Funktionen entstehen, Göttingen 1881.
- Zur Theorie der linearen Differentialgleichungen, Berlin 1901.
- Gesammelte Werke, Hrsg. von Richard Fuchs und Ludwig Schlesinger. 3 Bde. Berlin 1904–1909.
- Jeremy Gray (1984). "Fuchs and the theory of differential equations". Bulletin AMS (New Series). 10 (1): 1–26. MR 722855.
- G. B. Mathews (1902) Lazarus Fuchs Nature 66:156,7 (#1702).
- O'Connor, John J.; Robertson, Edmund F., "Lazarus Fuchs", MacTutor History of Mathematics archive, University of St Andrews.
- Lazarus Fuchs at the Mathematics Genealogy Project
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