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Rational approximation to solutions of linear differential equations with algebraic coefficients

Rational approximation to solutions of linear differential equations with algebraic coefficients

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding="application/x-tex">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be the field of formal series <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="alpha equals a Subscript k Baseline t Superscript k Baseline plus midline-horizontal-ellipsis plus a 0 plus a Subscript negative 1 Baseline t Superscript negative 1 Baseline …