Word Count : 173

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Consider the generating function of Hermite polynomials [ e^{2xt-t^2}=\sum_{n=0}^{\infty}H_n(x)\frac{t^n}{n!}. ] Write a similar generating function with another parameter (s): [ e^{2xs-s^2}=\sum_{m=0}^{\infty}H_m(x)\frac{s^m}{m!}. ] Multiply the two generating functions: [ e^{2xt-t^2},e^{2xs-s^2}=e^{2x(t+s)-(t^2+s^2)}. ] Now multiply both sides by (e^{-x^2}) and integrate with respect to (x) over ____ ______ __________ ___ _____ ______ ______ ____.
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