Now I corrected my code to get the constant right.
At 1.5 there is a similarly "good" islog as there is at 0.
Moreover the effect indeed points toward a singularity of some isexp's at radius \( \approx 1.4 \). This cant be seen for the islog at 0 because isexp is then at -1 and can only have radius 1.
The following both conformal plots - first isexp at -1 (inv of islog at 0), second isexp at \( \approx 0.5 \) (inv of islog at 1.5); both are continued to the left and right by log and exp - show this similar limitation of the convergence radius which must be caused by a singularity.
The first picture (isexp@-1) shows the conformal map of (-1,1)x(0,0.9).
The second picture (isexp@0.5) shows the conformal map of (-1,1)x(0,1.4).
The singularity of isexp@-1 is -2 and causes the convergence radius to be 1.
The convergence radius of isexp@0.5 must be reduced to \( \approx 1.4 \) by some other singularity than -2.
At 1.5 there is a similarly "good" islog as there is at 0.
Moreover the effect indeed points toward a singularity of some isexp's at radius \( \approx 1.4 \). This cant be seen for the islog at 0 because isexp is then at -1 and can only have radius 1.
The following both conformal plots - first isexp at -1 (inv of islog at 0), second isexp at \( \approx 0.5 \) (inv of islog at 1.5); both are continued to the left and right by log and exp - show this similar limitation of the convergence radius which must be caused by a singularity.
The first picture (isexp@-1) shows the conformal map of (-1,1)x(0,0.9).
The second picture (isexp@0.5) shows the conformal map of (-1,1)x(0,1.4).
The singularity of isexp@-1 is -2 and causes the convergence radius to be 1.
The convergence radius of isexp@0.5 must be reduced to \( \approx 1.4 \) by some other singularity than -2.