Ramanujan wins again!! @drpeyam

Uploaded December 2024 | Updated September 2026, 1 week ago

Ramanujan would be proud!!

We calculate the integral from 0 to infinity of sin x^n using Ramanujan's master theorem. This involves by writing the function out as a Taylor or Maclaurin series and then converting it into the Gamma function, which is a generalization of the factorial function. We also use Euler's formula which relates the gamma function with sin and cos. This is a must see for anyone who appreciates Srinivasa Ramanujan's work and math and calculus in general

Complex Analysis Way: youtu.be/ur9tOdkvrTQ

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$Inhomogeneous case Laplace transform and differential equations We use the Laplace transform to solve differential equations. The good news is that the same technique used to solve homogeneous ODE also works for inhomogeneous differential equations: Take the Laplace transform, solve for it, and then apply the partial fractions technique to find the inverse Laplace transform. This is a must-see for any mathematician, physicist, or engineer, enjoy! What is the Laplace transform: https://youtu.be/NmluV31oHq8 Laplace transform example: https://youtu.be/BHGnFcGhR5w Laplace transform playlist:https://www.youtube.com/playlist?list=PLJb1qAQIrmmB3NiV7Fy0tWcSmAYLQ7SCS Subscribe to my channel: https://youtube.com/drpeyam Instagram: https://www.instagram.com/peyamstagram/ Teespring merch: https://dr-peyam.creator-spring.com/?$

Two complex solutions in x^2021=x^2020+1

Peyam goes PUTNAM: Destroying a Monster Polar Integral (2021 Putnam A4)