Derivative recurrence relation for Hermite polynomials
Posted by peeterjoot on January 3, 2012
For a QM problem I had need of a recurrence relation for Hermite polynomials. I found it in , but thought I’d try to derive the relation myself.
The starting point I’ll use is the Rodgigues’ formula definition of the Hermite polynomials
Let’s write , and take the derivative of
So we have the rather simple end result
 M. Abramowitz and I.A. Stegun. Handbook of mathematical functions with formulas, graphs, and mathematical tables, volume 55. Dover publications, 1964.