I would like an opinion on this issue: similarly to the fact that $$F(z|m)=x\Longleftrightarrow z=\text{am}(x|m)$$
I also tried to reverse the function $E(z|m)$ and got the following series (I arbitrarily called $\text{bm}(x|m)$ the inverse)
$$E(z|m)=x\Longleftrightarrow z=\text{bm}(x|m)$$
$$\text{bm}(x|m)\propto x+\frac{mx^{3}}{3!}+\frac{m(13m^{2}-4)}{5!}x^{5}+\frac{m(493m^{2}-284m+16)}{7!}x^{7}+\frac{m(37369m^{3}-31224m^{2}+4944m-64)}{9!}x^{9}+\tfrac{m(4732249m^{4}-5165224m^{3}+1406832m^{2}-81088m+256)}{11!}x^{11}+\tfrac{m(901188997m^{5}-1212651548m^{4}+474297712m^{3}-56084992m^{2}+1306880m-1024)}{13!}x^{13}+\tfrac{m(240798388357m^{6}-384956066148m^{5}+197165292576m^{4}-36844921856m^{3}+2119725312m^{2}-20954112m+4096)}{15!}x^{15}+\;...$$ For $|x|<\dfrac{\pi}{2}$
I can't see useful recurring patterns to search the closed formula, does anyone have any suggestions?
