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Schläfli's work was in geometry, arithmetic and function theory. He gave the integral representation of the Bessel function and of the gamma function. He also worked on elliptic modular functions.
Schläfli made an important contribution to non- Euclidean (elliptic) geometry when he proposed that spherical three-dimensional space could be regarded as the surface of a hypersphere in Euclidean four-dimensional space.
He became professor of mathematics at Bern and Theory of continuous manifolds was published in 1901 after his death.
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