Generating function for Hermite (physicist) polynomials

Theorem

The following formula holds: $$\exp \left(2xt-t^2 \right) = \displaystyle\sum_{k=0}^{\infty} \dfrac{H_k(x)t^k}{k!},$$ where $\exp$ denotes the exponential, $H_k$ denotes the physicist's Hermite polynomials, and $k!$ denotes the factorial.

References

• 1960: Earl David Rainville: Special Functions ... (previous) ... (next): $103. (1)$