What Lies *Between* a Function and Its Derivative?

Try Brilliant's tutor for free: https://brilliant.org/BriTheMathGuy/ . You’ll also get 20% off an annual Premium subscription. You know the first and second derivatives, but with the Gamma function you can take half a derivative, and applying it twice gives back the ordinary one. CHAPTERS 0:00 - What lies between? 0:39 - A 300-year-old question 1:22 - The obvious guess 2:23 - Where coefficients come from 2:59 - Gamma to the rescue 3:33 - Taking half a derivative 4:47 - x squared, recovered 5:03 - Exponentials and sine 6:00 - The dial 6:27 - Nobody can draw it 7:08 - Riemann-Liouville 7:34 - The constant shock 7:57 - Fractional derivatives have memory 8:50 - Why anyone cares 9:17 - Today's sponsor: Brilliant 10:49 - The dial, recapped This video was partially created using Manim. This video was sponsored by Brilliant. Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. #math #mathematics #brithemathguy