Ziv's Math World

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1. Argument by Contradiction

Problem 1: Determine all functions satisfying     for all positive integers and . idea and solution: We could attempt some functions. We find that constant function works, does not work. does not work. This prompt us, maybe the only possible solution is ? This is because the left and right hand side has different…

March 2025
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  • 1. Argument by Contradiction

    Problem 1: Determine all functions satisfying     for all positive integers and . idea and solution: We could attempt some functions. We find that constant function works, does not work. does not work. This prompt us, maybe the only possible solution is ? This is because the left and right hand side has different […]

    ../..

  • 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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