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How to understand Weierstrass infinite product?
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
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An approximation problem
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
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How to understand Weierstrass infinite product?
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…