Physics – Quantum Physics
Scientific paper
1995-06-07
Phys.Lett. A208 (1995) 8
Physics
Quantum Physics
LaTeX, 8 pages
Scientific paper
10.1016/0375-9601(95)00761-Q
For use in calculating higher-order coherent- and squeezed- state quantities, we derive generalized generating functions for the Hermite polynomials. They are given by $\sum_{n=0}^{\infty}z^{jn+k}H_{jn+k}(x)/(jn+k)!$, for arbitrary integers $j\geq 1$ and $k\geq 0$. Along the way, the sums with the Hermite polynomials replaced by unity are also obtained. We also evaluate the action of the operators $\exp[a^j(d/dx)^j]$ on well-behaved functions and apply them to obtain other sums.
Nieto Michael Martin
Truax Rodney D.
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