Lazarus Fuchs, Date of Birth, Place of Birth, Date of Death

    

Lazarus Fuchs

German mathematician

Date of Birth: 05-May-1833

Place of Birth: Mosina, Greater Poland Voivodeship, Poland

Date of Death: 26-Apr-1902

Profession: teacher, mathematician, university teacher

Nationality: Germany

Zodiac Sign: Taurus


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About 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 (Mosina) (located in Grand Duchy of Posen) 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. 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 {\displaystyle 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 = ? n = 0 8 a j , n ( x - x 0 ) n + s j , a 0 ? 0 j = 1 , 2. {\displaystyle y_{j}=\sum _{n=0}^{\infty }a_{j,n}(x-x_{0})^{n+\sigma _{j}},\quad a_{0}\neq 0\,\quad j=1,2.} where the exponents s j {\displaystyle \sigma _{j}} can be determined from the equation.
  • In the case when s 1 - s 2 {\displaystyle \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 ( d y d z , y , z ) = 0 {\displaystyle F\left({\frac {dy}{dz}},y,z\right)=0} to be free of movable singularities. Lazarus Fuchs was the father of Richard Fuchs, a German mathematician.

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