Geodesic
Pad\'e-approximations to solutions of differential equations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 2, pp. 527-537.

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The Padé–Hermite's approximations to solutions of linear homogeneous differential equations of the second order with coefficients — rational functions in $z$ are found. We use only the general properties of differential and recurrent equations but not the explicit form of these solutions. 
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Yu. N. Makarov. Pad\'e-approximations to solutions of differential equations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 2, pp. 527-537. http://geodesic.mathdoc.fr/item/FPM_1999_5_2_a9/