Polynomial parametrisation of the canonical iterates to the solution of $-\gamma g^{\prime }=g^{-1}$

Abstract

The iterates $h_0,h_1,h_2,\dots$ constructed in [8,5] and converging to the only solution $g=h:[0,1]\to [0,1]$ of the iterative differential equation $-\gamma g^{\prime }=g^{-1}$, $\gamma >0$, are parametrised by polynomials over $\mathbb{Q}$, and the corresponding constant $\gamma =\kappa \approx 0.278877$ is estimated by rational numbers.

7 pages, 1 figure, 2 tables