Uploaded February 2022 | Updated September 2026, 1 week ago
Defining the half integral, which is halfway between a function and its integral. Done by analogy with half derivatives, by finding formulas for the derivatives of power functions. It uses the factorial which is then generalized to the gamma function with Gaussian integrals. I also mention trig functions and applications to broken processes. This is a delight for any calculus student or anyone who is interested in fractional derivatives.
0:00 Introduction
0:30 Analogy
2:58 Gamma Function
5:00 Half integral of x
9:37 Properties and Applications
Half Derivative: youtu.be/gaAhCTDc6oA
YT channel: youtube.com/drpeyam
TikTok channel: tiktok.com/@drpeyam
Instagram: instagram.com/peyamstagram
Twitter: twitter.com/drpeyam
Teespring merch: teespring.com/stores/dr-peyam
Defining the half integral, which is halfway between a function and its integral. Done by analogy with half derivatives, by finding formulas for the derivatives of power functions. It uses the factorial which is then generalized to the gamma function with Gaussian integrals. I also mention trig functions and applications to broken processes. This is a delight for any calculus student or anyone who is interested in fractional derivatives.
0:00 Introduction
0:30 Analogy
2:58 Gamma Function
5:00 Half integral of x
9:37 Properties and Applications
Half Derivative: youtu.be/gaAhCTDc6oA
YT channel: youtube.com/drpeyam
TikTok channel: tiktok.com/@drpeyam
Instagram: instagram.com/peyamstagram
Twitter: twitter.com/drpeyam
Teespring merch: teespring.com/stores/dr-peyam
