Derivative of exp^[1/2] at the fixed point?

[sheldonison]

The 5 th derivative
of \( \approx \left(4.44695n+1.05794ni\right)^{z-L} \) is equal to

of \( \approx \left(4.44695n+1.05794ni\right)^{z-L} ln(4.44 n + 1.05 n i)^5 \)

??

No singularity ?

Im sure you make sense , but it is not clear what you are doing to me.

Regards

Tommy1729

I apologize for the typos, which I corrected. The correct equation is (z-L)^p, where (z-L) is being raised to a complex power.
\( h_k(z) \approx h(z) + c \cdot (z-L)^{(4.44695+1.05794i )}\;\;\;\; \) p ~= 4.44695+1.05794i is the pseudo period of sexp


The fifth derivative has the real part of the power term negative, so the value is no longer defined at L, just like \( z^{-0.553}=\frac{1}{z^{0.553}} \) is not continuous at z=0.
But the first four derivatives are defined and equal to zero at L.