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Zbl 0810.05009
Duverney, Daniel
Padé approximants and $U$- derivation. (Approximants de Padé et $U$-dérivation.) (French)
[J] Bull. Soc. Math. Fr. 122, No.4, 553-570 (1994). ISSN 0037-9484

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 $$\sum\sp{+\infty}\sb{n=1} X\sp n/u\sb n\quad\text{and}\quad 1+ \sum\sp{+\infty}\sb{n=1} X\sp n/(u\sb 1 u\sb 2\dots u\sb n)$$ in case $u\sb{n+1}= qu\sb n+ r$, $q\in K\sp*$, and we give an upper bound for the rest of these approximants when $K$ possesses an absolute value $\vert\ \vert$.

MSC 2000:: *05A30 q-calculus and related topics
33C65 Appell, Horn and Lauricella functions
05E35 Orthogonal polynomials (combinatorics)
41A21 Pade approximation

Keywords: Padé approximants; $U$-derivation; orthogonal polynomials; Padé table; formal series; approximants

Cited in: Zbl 0867.11054 Zbl 0852.11035

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