Lazarus Fuchs

{{Infobox scientist

| name = Lazarus Fuchs

| image = Lazarus Fuchs (HeidICON 33457) (cropped).jpg

| image_size =

| caption = Fuchs in 1884

| birth_date = {{birth date|df=y|1833|5|5}}

| birth_place = Moschin, Grand Duchy of Posen, Kingdom of Prussia

| death_date = {{death date and age|df=y|1902|4|26|1833|5|5}}

| death_place = Berlin, Kingdom of Prussia, German Empire

| citizenship =

| nationality = German

| ethnicity =

| fields =

| workplaces = University of Greifswald
University of Heidelberg
University of Berlin
University of Göttingen

| alma_mater = University of Berlin

| doctoral_advisor = Karl Weierstraß

| academic_advisors =

| doctoral_students = Gerhard Hessenberg
Edmund Landau
Hermann Schapira
Ludwig Schlesinger
Issai Schur
Theodor Vahlen
Ernst Zermelo

| notable_students =

| known_for = Fuchs relation
Fuchs's theorem
Fuchsian groups
Fuchsian model
Fuchsian theory
Picard–Fuchs equation

| author_abbrev_bot =

| author_abbrev_zoo =

| awards =

| religion =

| signature =

| footnotes =

}}

Lazarus Immanuel Fuchs (5 May 1833 – 26 April 1902) was a Jewish-German{{MacTutor|id=Fuchs|title=Lazarus Immanuel Fuchs}} mathematician who contributed important research in the field of linear differential equations.{{cite journal|author=Wilczynski, E. J.|author-link=Ernest Julius Wilczynski|title=Lazarus Fuchs|journal=Bull. Amer. Math. Soc.|year=1902|volume=9|issue=1|pages=46–49|mr=1557937|doi=10.1090/s0002-9904-1902-00952-x|doi-access=free}} 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

: $y''+p(x)y'+q(x)y=0$

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

: $y_j=\sum_{n=0}^\infty a_{j,n}(x-x_0)^{n+\sigma_j},\quad a_0\ne0\,\quad j=1,2.$

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

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

to be free of movable singularities.

An interesting remark about him as a teacher during the period of his work at the Heidelberg University 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 {{ill|Richard Fuchs (mathematician)|lt=Richard Fuchs|de|Richard Fuchs (Mathematiker)}}, 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

{{Commons category-inline|Lazarus Immanuel Fuchs}}
{{cite journal|author=Jeremy Gray|title=Fuchs and the theory of differential equations|journal=Bulletin of the AMS |series=New Series|year=1984|volume=10|issue=1|pages=1–26|mr=722855|doi=10.1090/S0273-0979-1984-15186-3|author-link=Jeremy Gray|doi-access=free}}
G. B. Mathews (1902) [http://www.nature.com/nature/journal/v66/n1702/pdf/066156b0.pdf Lazarus Fuchs] Nature 66:156,7 (#1702).
{{MacTutor|id=Fuchs}}
{{MathGenealogy|id=11370}}

Category:1833 births

Category:1902 deaths

Category:19th-century German Jews

Category:Converts to Lutheranism from Judaism

Category:People from Poznań County

Category:People from the Grand Duchy of Posen

Category:Humboldt University of Berlin alumni

Category:Academic staff of the University of Greifswald

Category:19th-century German mathematicians

Category:20th-century German mathematicians

Category:Hyperbolic geometers

Category:19th-century Lutherans

Category:Members of the Göttingen Academy of Sciences and Humanities

Category:Members of the Royal Society of Sciences in Uppsala

Category:Mathematicians from the Kingdom of Prussia

Category:Mathematicians from the German Empire