a mathematically stunning formula @drpeyam

Uploaded April 2023 | Updated September 2026, 1 week ago

a mathematically stunning formula. I find the formula for the second derivative of the gamma function at 1 which gives you pi^2/6 plus the euler mascheroni constant squares. This gives a beautiful identity that relates two mysterious constants. The gamma function is a generalization of the factorial which is used to count permutations and combinations. This is related to nice integrals using logarithmic and exponential functions. A must see for calculus students and anyone who is interested in math and sciences. It involves the Hurwitz and the Riemann zera functions and might be related to the Riemann hypothesis

Integral e^-x ln(x) youtu.be/80_fNEflUdw

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infinitely many people failed this interview question

$Solving the logistic equation Solving the logistic equation. What does the fox say? Here I solve a differential equation using separation of variables and partial fractions and integrals. It models the population of bunnies but with a limited factor. It gives a surprisingly good model approximation of populations like in Belgium. Enjoy this calculus adventure Subscribe to my channel: https://youtube.com/drpeyam TikTok: https://www.tiktok.com/@drpeyam Instagram: https://www.instagram.com/peyamstagram/ Twitter: https://twitter.com/drpeyam Teespring merch: https://teespring.com/stores/dr-peyam$

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