Difference between revisions of "Generating function for Hermite (physicist) polynomials"
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Latest revision as of 22:55, 8 July 2016
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.
Proof
References
- 1960: Earl David Rainville: Special Functions ... (previous) ... (next): $103. (1)$
