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Calculus of functions of complex variables

Limit of a function of a complex variable

Let f(z) be a single valued function defined at all points in some neighborhood of a point z0. Then the limit of f(z) as z approaches z0 is w0.
lim f(z) = w0
z→z0

Continuity

f(z) is said to be continuous at z = z0 if
lim f(z) = f(z0)
z→z0

Differentiability

Let f(z) be a single valued function of the variable z then
f'(z) = lim [f(z + δz) - f(z)]/δz
        δz→0
provided that the limit exist and is independent of the path along which δz → 0.



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