Differential equations for algebraic functions

  title={Differential equations for algebraic functions},
  author={Alin Bostan and Fr{\'e}d{\'e}ric Chyzak and Bruno Salvy and Gr{\'e}goire Lecerf and {\'E}ric Schost},
It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions. We show that the linear differential equation of minimal order has coefficients whose degree is cubic in the degree of the function. We also show that there exists a linear differential equation of order linear in the degree whose coefficients are only of quadratic degree. Furthermore, we prove… CONTINUE READING
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Calcul pratique des coefficients de Taylor d’une fonction algébrique

L. Comtet
Enseignement Math. (2), 10:267–270, • 1964
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