Lazarus Fuchs

Lazarus Immanuel Fuchs (5 May 1833 – 26 April 1902) was a Jewish-German mathematician who contributed important research in the field of linear differential equations. He was born in Moschin in the Grand Duchy of Posen (modern-day Mosina, Poland) 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.

Contribution

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

$y^{″}+p(x)y^{\prime }+q(x)y=0$

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

$y_j=\sum _{n=0}^{\mathrm{\infty }}{a}_{j,n}(x-x_0{)}^{n+{\sigma }_j},a_0\ne 0j=1,2.$

where the exponents ${\sigma }_j$ can be determined from the equation. In the case when ${\sigma }_1-{\sigma }_2$ 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

$F(\frac{dy}{dz},y,z)=0$

to be free of movable singularities.

An interesting remark about him as a teacher during the period of his work at the Heidelberg University pertains to his manner of lecturing: his knowledge of the mathematics he was assigned to teach was so deep that he would not prepare before giving a lecture — he would simply improvise on the spot, while exposing the students to the train of thought taken by mathematicians of the finest degree.

Lazarus Fuchs was the father of Template:Ill, 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.

External links

• Template:Commons category-inline
• G. B. Mathews (1902) Lazarus Fuchs Nature 66:156,7 (#1702).
• Template:PAGENAMEBASE at the Mathematics Genealogy ProjectTemplate:EditAtWikidata

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