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InertialObservr's profile
〈 Berger | Dillon 〉
〈 Berger | Dillon 〉
〈 Berger | Dillon 〉
@InertialObservr

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〈 Berger | Dillon 〉

@InertialObservr

PhD student of Theoretical Particle Physics @UCIrvine l @NSF Fellow l Physics & Math Animations l Patreon: https://www.patreon.com/inertialobserver …

DC → CA
youtube.com/c/InertialObse…
Joined August 2015

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    1. 〈 Berger | Dillon 〉‏ @InertialObservr 16 Dec 2019
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      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

      6 replies 61 retweets 343 likes
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    2. Ricardo Pérez-Marco‏ @rperezmarco 16 Dec 2019
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      Replying to @InertialObservr

      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.

      2 replies 0 retweets 6 likes
    3. 〈 Berger | Dillon 〉‏ @InertialObservr 16 Dec 2019
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      Replying to @rperezmarco

      But these expansions do include the exponential factors. I just happened to pick a couple examples where they simplify nicelypic.twitter.com/gJMH3QGlHr

      1 reply 0 retweets 13 likes
    4. Ricardo Pérez-Marco‏ @rperezmarco 16 Dec 2019
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      Replying to @InertialObservr

      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.

      2 replies 0 retweets 4 likes
      〈 Berger | Dillon 〉‏ @InertialObservr 16 Dec 2019
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      Replying to @rperezmarco

      i see .. what is the definition of of the "order" of an entire function?

      1:12 PM - 16 Dec 2019
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      • John V
      2 replies 0 retweets 1 like
        1. Ricardo Pérez-Marco‏ @rperezmarco 16 Dec 2019
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          Replying to @InertialObservr

          https://proofwiki.org/wiki/Definition:Order_of_Entire_Function … You can study basic entire function theory in Ahlfors or Boas book.

          0 replies 1 retweet 6 likes
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        1. Rudy‏ @rudyroggio 16 Dec 2019
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          Replying to @InertialObservr @rperezmarco

          This is false. Reciprocal gamma is an entire function of order 1 and has a Weierstrass factorization.

          1 reply 0 retweets 0 likes
        2. Ricardo Pérez-Marco‏ @rperezmarco 16 Dec 2019
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          Replying to @rudyroggio @InertialObservr

          With exponential factors.pic.twitter.com/zb9LHJhNOa

          0 replies 0 retweets 1 like
          3. End of conversation

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