Lazarus_Fuchs

Lazarus Fuchs

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 x₀ is a regular singular point then the differential equation

$p(x)y''+q(x)y'+r(x)y=0\,$

has at least one solution of the form

$y=\sum_{n=0}^\infty a_n(x-x_0)^{n+\sigma},\quad a_0\ne0\,$

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

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