One of the famous expression of is     Here, we are writing as a some product of polynomials with zeros apparently shown. Remember that the right hand side has to be carefully chose to ensure its convergence. We are remained to consider: Can be factorize every entire function in the form of product of their zeros while maintaining its convergence? i.e. for any entire function, can be give the…

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Problem: Let us call an irrational number well approximated by rational numbers if for any natural numbers there exists a rational number such that     Solution: 1. Pick     Why does it work ? Let’s say we let . Then we have     and     We now proceed in proving that when is large enough     We have     So we want    …

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