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Padé approximants and \(U\)- derivation. (Approximants de Padé et \(U\)-dérivation.) (French) Zbl 0810.05009

Summary: The notion of \(U\)-derivation allows us to construct explicitly sequences of formal orthogonal polynomials with respect to some linear forms of \(K[X]\), where \(K\) is an arbitrary commutative field. From this we get the diagonal of the Padé table of the formal series \[ \sum^{+\infty}_{n=1} X^ n/u_ n\quad\text{and}\quad 1+ \sum^{+\infty}_{n=1} X^ n/(u_ 1 u_ 2\dots u_ n) \] in case \(u_{n+1}= qu_ n+ r\), \(q\in K^*\), and we give an upper bound for the rest of these approximants when \(K\) possesses an absolute value \(|\;|\).

MSC:

05A30 \(q\)-calculus and related topics
33C65 Appell, Horn and Lauricella functions
05E35 Orthogonal polynomials (combinatorics) (MSC2000)
41A21 Padé approximation
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References:

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