Geodesic
Asymptotics for quadratic Hermite-Padé polynomials associated with the exponential function
Electronic transactions on numerical analysis, Tome 14 (2002), pp. 195-222.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The asymptotic behavior of quadratic Hermite-Pad$\acute e$ polynomials p , q , r $\in P$ of type I and p , n n n n n q , r $\in P$ of type II associated with the exponential function are studied. In the introduction the background of n n 2n the definition of Hermite-Pad$\acute e$ polynomials is reviewed. The quadratic Hermite-Pad$\acute e$ polynomials p , q , r $\in P$ n n n n of type I are defined by the relation p (z) + q (z)ez + r (z)$e2z = O(z3n+2)$ as z $\rightarrow 0$, n n n and the polynomials p , q , r $\in P$ of type II by the two relations n n n 2n p (z)ez - q (z) = $O(z3n+1)$ as z $\rightarrow 0$, n n p (z)e2z - r (z) = $O(z3n+1)$ as z $\rightarrow 0$.
Classification : 41A21, 30E10
Keywords: quadratic Hermite-pad$\acute e$ polynomials of type I and type II, the exponential function, German and Latin polynomials, Hermite-pad$\acute e$ approximants 
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     author = {Stahl, Herbert},
     title = {Asymptotics for quadratic {Hermite-Pad\'e} polynomials associated with the exponential function},
     journal = {Electronic transactions on numerical analysis},
     pages = {195--222},
     publisher = {mathdoc},
     volume = {14},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2002__14__a1/}
}
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Stahl, Herbert. Asymptotics for quadratic Hermite-Padé polynomials associated with the exponential function. Electronic transactions on numerical analysis, Tome 14 (2002), pp. 195-222. http://geodesic.mathdoc.fr/item/ETNA_2002__14__a1/