Problem 1760 (difficulty: 6/10)

If the zeros of the regular \(\displaystyle f: S(0, 1) \to S(0, 1)\) function are \(\displaystyle |a_k|<1\) complex numbers (possibly infinitely many), then

\(\displaystyle |f(0)|\le \left|\prod\limits_{i=0}^\infty a_i\right|.\)

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