Lazarus Immanuel Fuchs (5 May 1833 – 26 April 1902) was a

Jewish-German The history of the Jews in Germany goes back at least to the year 321 CE, and continued through the Early Middle Ages (5th to 10th centuries CE) and High Middle Ages (c. 1000–1299 CE) when Jewish immigrants founded the Ashkenazi Jewish comm ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

who contributed important research in the field of

linear differential equation In mathematics, a linear differential equation is a differential equation that is linear equation, linear in the unknown function and its derivatives, so it can be written in the form a_0(x)y + a_1(x)y' + a_2(x)y'' \cdots + a_n(x)y^ = b(x) wher ...

s. He was born in Moschin in the

Grand Duchy of Posen The Grand Duchy of Posen (; ) was part of the Kingdom of Prussia, created from Prussian Partition, territories annexed by Prussia after the Partitions of Poland, and formally established following the Congress of Vienna in 1815. On 9 February 1 ...

(modern-day Mosina, Poland) and died in

Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...

Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...

. He was buried in

Schöneberg Schöneberg () is a locality of Berlin, Germany. Until Berlin's 2001 administrative reform it was a separate borough including the locality of Friedenau. Together with the former borough of Tempelhof it is now part of the new borough of Te ...

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 group In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R). The group PSL(2,R) can be regarded equivalently as a group of orientation-preserving isometries of the hyperbolic plane, or conformal transformations of the unit disc, or co ...

s and functions, and the

Picard–Fuchs equation In mathematics, the Picard–Fuchs equation, named after Émile Picard and Lazarus Fuchs, is a linear ordinary differential equation whose solutions describe the periods of elliptic curves. Definition Let :j=\frac be the j-invariant with g_2 and ...

. A singular point ''a'' of a

y''+p(x)y'+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_^\infty a_(x-x_0)^,\quad a_0\ne0\,\quad j=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\left(\frac,y,z\right)=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 Heidelberg University, officially the Ruprecht Karl University of Heidelberg (; ), is a public research university in Heidelberg, Baden-Württemberg, Germany. Founded in 1386 on instruction of Pope Urban VI, Heidelberg is Germany's oldest unive ...

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 , 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

External links

* * * G. B. Mathews (1902
Lazarus Fuchs

Nature Nature is an inherent character or constitution, particularly of the Ecosphere (planetary), ecosphere or the universe as a whole. In this general sense nature refers to the Scientific law, laws, elements and phenomenon, phenomena of the physic ...

66:156,7 (#1702). * * 1833 births 1902 deaths 19th-century German Jews Converts to Lutheranism from Judaism People from Poznań County People from the Grand Duchy of Posen Humboldt University of Berlin alumni Academic staff of the University of Greifswald 19th-century German mathematicians 20th-century German mathematicians Hyperbolic geometers 19th-century Lutherans Members of the Göttingen Academy of Sciences and Humanities Members of the Royal Society of Sciences in Uppsala Mathematicians from the Kingdom of Prussia Mathematicians from the German Empire {{Germany-mathematician-stub