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Fig.1. Quadratic function (black curve) and two its superfunctions
Fig.2. $u\!+\mathrm i v=\mathrm{SdPow}_2(x\!+\mathrm i y)$

SdPow is specific superpower function, id est, the superfunction of the power function $~z\mapsto z^a\!=\!\exp(\ln(z) \,a)~$

For given parameter $a$,


Usually, it is assumed, that $a\!>\!1$.

Transfer function

Function $F\!=\!\mathrm{SdPow}_a$ is superfunction for the specific power function $T(z)\!=\!z^a$. The superfunction satisfies the transfer equation


For this specific transfer function $T$, the two real-holomorphix solutions are SuPow and SdPow:



For the power function both, the superfunctions and the Abel functions can be expressed as elementary functions. For $a\!=\!2$, these functions are who functions are shown in Fig.1.

For the same $a\!=\!2$, the complex map of function SdPow is shown in FIg.2.



AdPow, Elementary function, Power function, SdPow, SuPow, Superfunction Superpower