1550251515-Classical_Complex_Analysis__Gonzalez_

Elementary Fm1ctions 293

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Fig. 5.36

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Fig. 5.37

equivalent to the torus or anchor ring, and also topologically equivalent to
a sphere with a handle (Fig. 5.38).
The case w = *V,...a..,..(z~-~z~ 1 .,....)(,....z--~z-, 2 ),...,(-z---za'")...,..(z _ z 4 ), with all four roots

distinct, is essentially the same as the preceding case, since here we have
again four critical points, all of which are now finite. Hence, for the Rie-
mann surface in the case m = 4, we can take either of the surfaces shown
in Figs. 5.37 and 5.38.

Fig. 5.38