Faculty of Khan | Hermite Differential Equation and Hermite Polynomials @FacultyofKhan | Uploaded 3 years ago | Updated 5 minutes ago
In this video, I demonstrate how to solve the #HermiteODE using the #SeriesSolution method to obtain the #HermitePolynomials.

EDIT: At 1:40, I say that the derivative of the sum is the sum of the derivatives - this only applies for an infinite series if we're working within the radius of convergence. In this situation though, the radius of convergence can be infinite since the ODE doesn't have any singularities. Thanks to Quinn Kolt in the comments for pointing this out!

Questions/requests? Let me know in the comments!

Pre-Reqs: This video in my 'Topics in ODEs playlist': youtube.com/watch?v=c3XtwTsE7QY&list=PLdgVBOaXkb9ATVsK2Q84ghjBgIk5faHNc&index=1
Lecture Notes: drive.google.com/file/d/1LAztdvb4J3dxEX2Bgwa-9-G6vZkrtTrY/view?usp=sharing
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan

Special thanks to my Patrons for supporting me at the $5 level or higher:
Daigo Saito
Patapom
Charles Twardy
Michael Mark
Alec Dinerstein
Yenyo Pal
Lisa Bouchard
Eugene Bulkin
Rene Gastelumendi
Borgeth
Jacob Soares
Kelvin Xie
Nidhi Rathi
Andy Johnston
Ike J.
K2c2321