log(z)
Assuming "log" is the natural logarithm | Use instead

Input

log(z)

Plot

Plot
Plot

Complex map

Complex map

Root

z = 1

Branch point

z = 0

Derivative

d/dz(log(z)) = 1/z

Indefinite integral

integral log(z) dz = z (log(z) - 1) + constant (assuming a complex-valued logarithm)

Alternative representation

log(z) = log(e, z)
log(z) = log(a) log(a, z)
log(z) = -Li_1(1 - z)
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