= Entire functions with the same zero divisor
{title2=$f=e^h g,\qquad h\ {\rm unique\ modulo}\ 2\pi i\mathbb Z$}
If two nonzero <entire functions> have identical zeros and orders, their quotient extends to a nowhere-zero <entire function>. Its logarithmic derivative has a primitive on the simply connected plane, producing a <holomorphic logarithm> $h$ and the displayed relation. Any two choices differ by one constant integer multiple of $2\pi i$. On a multiply connected domain the logarithm can fail to exist globally.
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