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    Normalization of Hermite Polynomials

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    Knowing that {Hn}, n = 0, 1, 2... are orthogonal and
    (Ho, Ho) = sqrt pi, (Hn, Hn) = 2n(Hn-1, Hn-1), nEN

    with respect to a suitable weight function p(x), write down first two orthonormal Hermite polynomials.

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    Solution Preview

    You just have to normalize them so that the norm becomes 1.

    So, (H0,H0) = ...

    Solution Summary

    We explain how to obtain the proper normalization of the Hermite polynomials.