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Is it possible to write $f(n,m,\alpha,\beta)$ as a fraction, i.e. $\frac{a+ib}{c}$, where a,b and c are integers?

$$f(n,m,\alpha,\beta) = H_{-1-m}(\frac{\alpha + i\beta}{\sqrt 2})$$

where $i$ is the imaginary unit and $H_n(x)$ is the nth Hermite polynomial in x and

$$ n \in \mathbb{N} \land m \in \{0,1,2,3\} \land \alpha \in \mathbb{Q} \land \beta \in \mathbb{Q} $$

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$H_{-1}, \ldots, H_{-4}$ are not polynomials, assuming you're talking about the Hermite functions (what Maple calls $HermiteH(n,x)$). For example, $H(-1,t) = (1 - \text{erf}(t)) \sqrt{\pi} e^{t^2}/2$. –  Robert Israel Aug 2 '12 at 22:36
    
How did you get from HermiteH(n,x) to the example you provided? –  MarcF Aug 3 '12 at 8:46
    
In Maple 16, FunctionAdvisor(specialize,HermiteH(-1,t)); –  Robert Israel Aug 3 '12 at 18:21
    
Is there an equivalent tool in Mathematica? –  MarcF Aug 3 '12 at 21:10
    
It seems to be HermiteH there too. Wolfram Alpha gets the same formula for HermiteH[-1,t]. –  Robert Israel Aug 3 '12 at 21:25
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