When trying to solve this integral question ;
Integral $\int_0^1 \frac{\sqrt[4]{\ln(1+t)} +\sqrt {\ln(1+t)}}{t^2+1} dt$
.. I mentioned that the function $\sqrt {\ln(1+x)}$ is well studied and its Taylor or * more specific * Maclauren series have known coefficients. Some generalization of Bernouilli or Gregory coefficients.
However I also said I knew little about it and I could not find good references.
What are the closed forms and asymptotics ?
And how many recursion equations do they satisfy ?
As mentioned in the link, I am aware of Faa di bruno formula and the Lagrange inversion theorem.
Computing a few terms is not that hard, but I am looking for deeper insight.
