Why is the symbol ζ sometimes used in a complex function?

Question

I just flipped through a book on complex analysis and found some functions being written as f(ζ) instead of f(z). It did not state why this is so. Can someone help enlighten me? Thank you.

Answer 1

Zeta ($\zeta$) is the Greek letter corresponding to z. As far as I remember, it is often introduced when we are already using z (as in the Cauchy integration formula). -- sos440

When studying functions of one real variable one uses $x$, $t$, or $r$ (and other letters) as names for the independent variable. In the same way one uses $z$, $\zeta$, or $w$ (and other letters) as names for a complex independent variable. -- Christian Blatter

(Also, some people prefer using $w$ for dependent variable, as in $w=f(z)$; then $\zeta$ becomes the preferred choice for a second instance of independent variable.)