restricted position

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… ►(However, if we require a principal value to be single-valued, then we can restrict

-\pi<\operatorname{ph}z\leq\pi

.) … ►That is, given any positive number

\epsilon

, however small, we can find a positive number

\delta

such that

\left|f(z)-f(z_{0})\right|<\epsilon

for all

z

in the open disk

\left|z-z_{0}\right|<\delta

. … ►provided that in both cases

C

is described in the positive rotational (anticlockwise) sense. … ►A set of complex numbers

\{z_{m,n}\}

where

m

and

n

take all positive integer values is called a double sequence. It converges to

z

if for every

\epsilon>0

, there is an integer

N

such that …