Can anyone tell me how can I find the hermite representation of the function $x^2-c$? And it would be very interesting, if anyone could tell me a good source about the Hermite representation of a general function $f$? Thank you very much! Maybe I should add "my" definiton of the Hermite Polynomials: $H_{0}(x)=1$ and $H_{n}(x)=(-1)^{n}e^{\frac{x^2}{2}}\frac{d^{n}}{d^{n}x}\left(e^{-\frac{-x^2}{2}}\right)$ Unfortunately I can't find any useful sources about Hermite Polynomials.
Hermite representation
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sequences-and-series
power-series
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0You did compute $H_1$ and $H_2$? – 2012-11-04
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0$H_{1}(x)=x$ and $H_{2}(x)=x^{2}-1$ – 2012-11-04
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0Right, so now you have $1$, $x$ and $x^2-1$ and you're looking for a linear combination of these to form $x^2 - c$. Start at the highest degree monomial and work your way down. – 2012-11-04