Fuchsian

Lazarus Fuchs
Lazarus Immanuel Fuchs (1833–1902)
Born	(1833-05-05)5 May 1833 Moschin, Prussia
Died	26 April 1902(1902-04-26) (aged 68) Berlin, German Empire
Residence	Germany
Nationality	German
Alma mater	University of Berlin
Known for	Fuchsian groups Picard–Fuchs equation Fuchs's theorem
Scientific career
Institutions	University of Greifswald University of Heidelberg University of Berlin University of Göttingen
Doctoral advisor	Karl Weierstraß
Doctoral students	Gerhard Hessenberg Edmund Landau Hermann Schapira Ludwig Schlesinger Issai Schur Theodor Vahlen Ernst Zermelo
Influences	Ernst Kummer
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.

He is the eponym of Fuchsian groups and functions, and the Picard–Fuchs equation. A singular point a of a linear differential equation

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 ensure the existence of two linearly independent solutions of the form

where the exponents ${\displaystyle \sigma _{j}}$ can be determined from the equation. In the case when ${\displaystyle \sigma _{1}-\sigma _{2}}$ is an integer this formula has to be modified.