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Abel's theorem and the allied theory, including the theory of the theta functions (1897)

Baker, H. F. (Henry Frederick), 1866-1956 · Cambridge : University Press · leaf 586

An illustration from Abel's theorem and the allied theory, including the theory of the theta functions, 1897, leaf 586
Fig. 15. For instance the new loop [a^] in this diagram (Fig. 15) is a deformation of a loopwhich may be drawn as here (Fig. 16); … Fig. 16. since the integrand of the Abelian integral w^ is single-valued on the Eiemann surface,independently of the loops, the doubled portion from L to M is self-destructive ; anda circuit of this new loop [og] gives cor, 2 - <<>r, 1 > as desired. Hence the general transformation can…

Geometry, Algebraic · Functions, Theta

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