Cyklometrická funkce: Porovnání verzí

\arcsin x &{}= -\mathrm{i}\,\logln\left(i\,mathrm{i}x+\sqrt{1-x^2}\right) &{}\\[10pt]

\arccos x &{}= -i\,\log\left(x+\sqrt{x^2-1}\right) = \frac{\pi}{2}\,+\mathrm{i}\logln\left(\mathrm{i\,}x+\sqrt{1-x^2}\right) = \frac{\pi}{2}-\arcsin x &{}\\[10pt]

\mathrmoperatorname{arctg}x &{}= \frac{\mathrm{i}}{2}\left(\logln\left(1-i\,mathrm{i}x\right)-\logln\left(1+i\,mathrm{i}x\right)\right)= \mathrmoperatorname{arccotg}\frac{1}{x}\\[10pt]

\mathrmoperatorname{arccotg}x &{}= \frac{\mathrm{i}}{2}\left(\logln\left(1x-\fracmathrm{i}{x}\right)-\logln\left(1x+\fracmathrm{i}{x}\right)\right)= \mathrmoperatorname{arctg}\frac{1}{x}\\