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The Frobenius method can be used to represent solutions of ordinarydifferential equations by (generalized) power series. It is useful to haveprior knowledge of the coefficients of this series. In this contribution wedemonstrate that the magnitude of the coefficients can be predicted tosurprisingly high accuracy by a Legendre transformation of WKB approximatedsolutions to the differential equations.

Estimating Coefficients of Frobenius Series by Legendre Transform and WKB Approximation