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Elementary Functions > ArcSin[z] > Visualizations

Riemann surfaces (4 graphics)

Real and imaginary parts of the continuation of over the . The real part is a faithful representation of the Riemann surface of .

Real part of the continuation of over the . The connections between the sheets along the branch cuts and the branch points at of square root type are clearly visible. The viewpoint is from the lower halfplane.

Real parts of the continuation of over the Riemann sphere. The branch points are at the north pole (logarithmic branch point) and at the intersection of the equator with the ‐plane (two square root branch points).