On a sequence of generalized Bers exponential functions with interior structure (Q1893640)

In the framework of his famous generalization of complex differentiation and integration, L. Bers in the fourties introduced and studied a sequence of functions, the generalized Bers powers, generalizing the functions \(c(x - x_0)^n\). Here the author constructs and studies generalized powers (!!, wrong translation!) with an interior structure: at a point \(x_b > x_0\) the generalized power function furcates (into branches), and (for a suitable choice of some free constants) a certain quantity of those branches joins again at \(x_j > x_b\) (and this procedure may be repeated). These functions preserve the properties of the Bers powers with respect to differentiation. Some results concerning the representation of these new functions are found, too. -- The author points out that there are physical arguments for the recent constructions -- may be.