Lazarus Fuchs

Infobox Scientist
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name = Lazarus Fuchs


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caption = Immanuel Lazarus Fuchs (1833–1902)
birth_date = 5 May 1833
birth_place = Mosina, Grand Duchy of Poznań
death_date = 26 April 1902
death_place = Berlin, Germany
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workplaces = University of Greifswald
University of Berlin
University of Göttingen
alma_mater = University of Berlin
doctoral_advisor = Karl Weierstraß
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doctoral_students = Gerhard Hessenberg
Edmund Landau
Issai Schur
Theodor Vahlen
Ernst Zermelo
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known_for = Fuchsian groups
Picard-Fuchs equation
Fuchs's theorem
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influences = Ernst Kummer
influenced = Jules Henri Poincaré
Marie Ennemond Camille Jordan
Felix Christian Klein
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Immanuel Lazarus Fuchs (5 May 1833 – 26 April 1902) was a German mathematician. He was born in Mosina (located in Grand Duchy of Poznań) and died in Berlin, Germany.

He is the eponym of Fuchsian groups and functions, and the Picard-Fuchs equation; "Fuchsian" differential equations are those with regular singularities. Fuchs is also known for Fuchs's theorem which states that if "x"₀ is a regular singular point then the differential equation

: $p(x)y"+q(x)y\text{'}+r(x)y=0,$

has at least one solution of the form

: $y=sum\_\{n=0\}^infty\; a\_n(x-x\_0)^\{n+sigma\},quad\; a\_0\; e0,$

for some "σ" to be determined. In some cases, there will be two linearly independent solutions of that form.

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