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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
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    3. Bobbie‏ @bobbielf2 Feb 28
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      • Report NetzDG Violation
      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
      〈 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

      5:02 PM - 28 Feb 2020
      • 1 Like
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      1 reply 0 retweets 1 like
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        1. 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
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