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If , 4, 8, ..., then terminates with the Power , and (normalized so that the Coefficient of is ) is the regular solution to the equation, known as the Hermite Polynomial. If , 6, 10, ..., then terminates with the Power , and (normalized so that the Coefficient of is ) is the regular solution to the equation, known as the Hermite Polynomial.

If , then Hermite's differential equation becomes

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1999-05-25