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where a is a positive integer greater than unity. This function is continuous within and on the boundary of the unit circle, is analytic within this circle, and cannot be continued analytically beyond it. I am indebted to Professor Hurwitz for an exceedingly simple proof of the principal theorem of my note, namely, that the inverse function is single-valued. The point to be established is that, z, z' being any two distinct points within or on the unit circle,

Note on the periodic developments of the equation of the center and of the logarithm of the radius vector