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- W1505200574 abstract "Tetration $F$ as the analytic solution of equations $F(z-1)=ln (F(z))$, $F(0)=1$ is considered. The representation is suggested through the integral equation for values of $F$ at the imaginary axis. Numerical analysis of this equation is described. The straightforward iteration converges within tens of cycles; with double precision arithmetics, the residual of order of 1.e-14 is achieved. The numerical solution for $F$ remains finite at the imaginary axis, approaching fixed points $L$, $L^{*}$ of logarithm ($L=ln L$). Robustness of the convergence and smallness of the residual indicate the existence of unique tetration $F(z)$, that grows along the real axis and approaches $L$ along the imaginary axis, being analytic in the whole complex $z$-plane except for singularities at integer the $z<-1$ and the cut at $z<-2$. Application of the same method for other cases of the Abel equation is discussed." @default.
- W1505200574 created "2016-06-24" @default.
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- W1505200574 date "2009-09-01" @default.
- W1505200574 modified "2023-09-27" @default.
- W1505200574 title "Solution of $F(z+1)=exp big (F(z)big )$ in complex $z$-plane" @default.
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- W1505200574 doi "https://doi.org/10.1090/s0025-5718-09-02188-7" @default.
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