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A simple recurrence relation for the even order moments of the Fabiusfunction is proven. Also, a very similar formula for the odd order moments interms of the even order moments is proved. The matrices corresponding to theseformulas (and their inverses) are multiplied so as to obtain a matrix thatcorrespond to a recurrence relation for the odd order moments in terms ofthemselves. The theorem at the end gives a closed-form for the coefficients.

A recurrence relation for the odd order moments of the Fabius function