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On a Special Nonlinear Functional Equation
1981
Proceedings of the Royal Society A
We study analytic solutions of the functional equation where c > 0 is a parameter, and constant solutions are excluded. I t suffices to consider solutions for which h(z) -z~l is regular in a neighbourhood of 2 = 0. If 0 < c ^ t, h(z) can be continued as a single-valued analytic function into the unit disc |s| < 1 where its only singularity is the pole a t 2 = 0; the circle \z\ = 1 is a natural boundary. On the other hand, if c > \, then by analytic continuation h(z) becomes a multiple-valued
doi:10.1098/rspa.1981.0146
fatcat:d7esytmt3ncatij6xxrkearqpy