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The generating function for Hermite polynomials is: $e^{-s^2+2s\xi} = \sum_{n=0}^{\infty}H_n(\xi) \frac{s^n}{n!}$. How does one do the power series expansion for $e^{-s^2+2s\xi}$?

David Kwak
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  • oh that’s easy. i thought had to treat $s$ like $x$ and did powers of $s$ – David Kwak Feb 10 '21 at 18:01
  • Introduction to Quantum Mechanics with Applications to Chemistry by Linus Pauling-E.Bright Wilson, McGraw-Hill 1935 : $\S$11c. Mathematical Properties of the Harmonic Oscillator Wave Functions. – Frobenius Feb 11 '21 at 01:10
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    Do you know how to expand $e^x$? Substitute $x\to-s^2+2s\xi$. – G. Smith Feb 10 '21 at 17:35

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