Weierstrass Factorization Theorem: Every entire function 𝑓(𝑧) can be 'factored' into a (possibly infinite) product of polynomials with the same zeroes as 𝑓(𝑧)pic.twitter.com/Te2YUrgP67
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Not exactly true. Only holds true for order <1 entire functions, otherwise you need exponential factors. In the Euler examples you can pair opposite root factors, or equivalently sin(sqrt(z))/sqrt(z) is of order 1/2<1.
But these expansions do include the exponential factors. I just happened to pick a couple examples where they simplify nicelypic.twitter.com/gJMH3QGlHr
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What I mean is that your statement that "Every entire function 𝑓(𝑧) can be 'factored' into a (possibly infinite) product of polynomials with the same zeroes as 𝑓(𝑧)" is not true.
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i see .. what is the definition of of the "order" of an entire function?
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