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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 Feb 28
      • Report Tweet
      • Report NetzDG Violation

      eⁱˣ = cos(x) + i sin(x)pic.twitter.com/4fCuF4LOY3

      44 replies 1,031 retweets 4,583 likes
      Show this thread
    2. 〈 Berger | Dillon 〉‏ @InertialObservr Feb 28
      • Report Tweet
      • Report NetzDG Violation

      A natural question is: Why is this animation smooth? The answer is that you can define the so-called fractional derivative, which generalizes nth derivative to a real number of derivatives The fractional Taylor series smoothly interpolates between integer derivativespic.twitter.com/757q5yvu7k

      12 replies 111 retweets 677 likes
      Show this thread
    3. Bobbie‏ @bobbielf2 Feb 28
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      Replying to @InertialObservr

      Well, I don't think you need fractional calculus at all, it just makes things unnecessarily complicated. I made the exact same animation simply by adding the next term in the Taylor series weighted by a number going from 0 to 1.

      1 reply 0 retweets 5 likes
    4. 〈 Berger | Dillon 〉‏ @InertialObservr Feb 28
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      Replying to @bobbielf2

      yes, you can interpolate any way you wish you can also make it by just replacing the n! with Γ(1+n) and summing over reals.. using the fractional derivative is more general it just happens that the fractional derivative of e^x is simple

      2 replies 0 retweets 8 likes
    5. Bobbie‏ @bobbielf2 Feb 28
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      Replying to @InertialObservr

      What do you mean by "summing over reals"?

      1 reply 0 retweets 1 like
    6. 〈 Berger | Dillon 〉‏ @InertialObservr Feb 28
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      Replying to @bobbielf2

      some evenly spaced sample like n=0 to n=20 in steps of 0.1

      1 reply 0 retweets 1 like
    7. Bobbie‏ @bobbielf2 Feb 28
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      Replying to @InertialObservr

      I see, so you mean applying trapezoidal rule to integrate the function x^t/Gamma(t+1). But this integral is only asymptotically approaching e^x for x going to infinity. For small x, you have no hope getting a good approximation. Have you really tried what you said?

      1 reply 0 retweets 2 likes
    8. Jason Hise‏ @JasonHise64 Mar 2
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      Replying to @bobbielf2 @InertialObservr

      Isn't the point of this animation to show how the approximation converges and gets better with more terms? It's plotting e^ix, and yes the initial frames of animation are very far from a unit circle and are thus a 'bad approximation' of e^ix, but I think that's missing the point.

      1 reply 0 retweets 0 likes
    9. Bobbie‏ @bobbielf2 Mar 2
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      Replying to @JasonHise64 @InertialObservr

      You don't understand asymptotic analysis. As a phd in math, I will tell you that calculating e^ix the way the OP claimed to be done is NOT going to converge for small x, no matter how many terms you take, aka the claim was false and he didn't understand what he was talking about.

      1 reply 0 retweets 0 likes
      〈 Berger | Dillon 〉‏ @InertialObservr Mar 2
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      Replying to @bobbielf2 @JasonHise64

      〈 Berger | Dillon 〉 Retweeted 黒木玄 Gen Kuroki

      Just because i don't walk you through every baby step doesn't mean i don't know what i'm talking abouthttps://twitter.com/genkuroki/status/1233657468409901056?s=20 …

      〈 Berger | Dillon 〉 added,

      黒木玄 Gen Kuroki @genkuroki
      #Julia言語 #julialang exp(it) (0 ≤ t ≤ 2π) のn次までのTaylor展開をnについて連続的に補間してプロット。 fractional derivative に基く補間になっている。 https://nbviewer.jupyter.org/gist/genkuroki/0daba234b8b7a15e6fcc2aca2ae205e2 … https://twitter.com/InertialObservr/status/1233502763339976704 … pic.twitter.com/NyTmSDMLlx
      Show this thread
      4:52 PM - 2 Mar 2020
      • 1 Retweet
      • 2 Likes
      • ソンツー(George) Songzhi Tao 黒木玄 Gen Kuroki
      1 reply 1 retweet 2 likes

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