# Lazarus Fuchs

**Lazarus Immanuel Fuchs** (5 May 1833 – 26 April 1902) was a Jewish-German[1] mathematician who contributed important research in the field of linear differential equations.[2] 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.

Lazarus Fuchs | |
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Lazarus Immanuel Fuchs (1833–1902) | |

Born | |

Died | 26 April 1902 68) | (aged

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 |

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 around 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 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.

Lazarus Fuchs was the father of Richard Fuchs, a German mathematician.

## Selected works

*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.

## References

- O'Connor, John J.; Robertson, Edmund F., "Lazarus Immanuel Fuchs",
*MacTutor History of Mathematics archive*, University of St Andrews. - Wilczynski, E. J. (1902). "Lazarus Fuchs".
*Bull. Amer. Math. Soc*.**9**(1): 46–49. doi:10.1090/s0002-9904-1902-00952-x. MR 1557937.

## External links

Media related to Lazarus Immanuel Fuchs at Wikimedia Commons - Jeremy Gray (1984). "
*Fuchs and the theory of differential equations*".*Bulletin of the AMS*. New Series.**10**(1): 1–26. doi:10.1090/S0273-0979-1984-15186-3. MR 0722855. - 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