Find the Hermite Polynomials of order 1 and 3.
Recall that the recurrence relations are given by
We have to evaluate these coefficients for k=1 and k=3, with initial conditions a0=0, a1=1.
Consequently all odd coefficients other than a1 will be zero. Since a0=0, all even coefficients will be zero, too. Thus
Consequently all odd coefficients other than a1 and a3 will be zero. Since a0=0, all even coefficients will be zero, too. Thus
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