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Königsberger worked on differential equations, influenced by Fuchs's function theory (he was a friend of Fuchs from his youth). His work on differential equations was influenced by Bunsen, Kirchhoff and Helmholtz, who he was close friends with in Heidelberg, and he considered the differential equations of analytic mechanics.
Königsberger is famed for his biography of Helmholtz (1902) and his biographical Festschrift for Jacobi (1904).
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