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Abstract: The asymptotic behavior of quadratic Hermite-Pade polynomials pn , qn , rn of type I and pn , qn , rn 2n of type II associated with the exponential function are studied. In the introduction the background of the definition of Hermite-Pade polynomials is reviewed. The quadratic Hermite-Pade polynomials pn , qn , rn of type I are defined by the relation pn (z) + qn (z)e + rn (z)e and the polynomials pn , qn , rn 2n of type II by the two relations qn (z) = O(z rn (z) = O(z 0. (Update)
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.... of quadratic HermitePad e polynomials of type II will be studied in the paper [23] First results are already contained in the paper [22]. The paper is organized as follows: The next section contains the statements and short discussions of all main results. In Section 3...
.... in [1] Detailed studies of quadratic approximants and especially the polynomials pn ; q n ; r n have been done in [3] 5] 6] [19], and [17] In [3] among other things, a 4 term recurrence relation together with very precise asymptotic estimates have been proved....
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2: Quadratic Hermite-Pade Approximants to the Exponential Function (context) - Stahl - 2002
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2: Szego, G., Uber einige Eigenschaften der Exponentialreihe, Sitzunggsberichte Berliner Math. Ges., 23(1924), 50-64.
BibTeX entry: (Update)
Stahl, H., Asymptotics for Quadratic Hermite-Pade Polynomials Associated with the Exponential Function, Electronic Trans. Num. Analysis (ETNA),14 (2002), 193-220. http://citeseer.ist.psu.edu/stahl02asymptotics.html More
@misc{ stahl02asymptotics,
author = "H. Stahl",
title = "Asymptotics for Quadratic {H}ermite-{Pad\'e} Polynomials Associated with the
Exponential Function",
journal = "Electronic Trans. Num. Analysis (ETNA)",
volume = "14",
pages = "193--220",
year = "2002",
url = "citeseer.ist.psu.edu/stahl02asymptotics.html" }
Citations (may not include all citations):64 Logarithmic Potentials with External Fields (context) - SAFF, TOTIK - 1997
42 Die Lehre von den Kettenbruchen (context) - PERRON - 1962
38 Cambridge University Press (context) - BAKER, GRAVES-MORRIS et al. - 1996
14 Multiple orthogonal polynomials (context) - APTEKAREV - 1998
12 Perfect systems (context) - MAHLER - 1968
10 Rational Approximation and Orthogonality (context) - NIKISHIN, SOROKIN - 1991
7 Allgemeine Theorie der kettenbruchahnlichen Algorithmen (context) - JACOBI
6 irrationality and transcendence (context) - VAN ASSCHE, polynomials - 1999
6 Asymptotics of Hermite-Pade polynomials (context) - APTEKAREV, STAHL - 1992
5 Sur la fonction exponentielle (context) - HERMITE
5 Quadratic Hermite-Pade approximation to the exponential func.. (context) - BORWEIN - 1986
5 Non-diagonal quadratic Hermite-Pade approximants to the expo.. (context) - DRIVER - 1995
5 On polynomials related with Hermite-Pade approximants to the.. - DRIVER, TEMME - 1998
4 Asymptotics of diagonal Hermite-Pade approximants to e (context) - WIELONSKY - 1997
4 Application of some formulas by Hermite to the approximation.. (context) - MAHLER - 1967
4 Zur Approximation der Exponentialfunktion und des Logarithmu.. (context) - MAHLER - 1931
3 A multidimensional generalisation of the Pade table (context) - JAGER - 1964
3 the zeros and poles of Pade approximants to e III (context) - SAFF, VARGA - 1978
3 the algebraic approximation of functions I -- IV (context) - COATES
3 Uber einige Eigenschaften der Exponentialreihe (context) - SZEG - 1924
1 Convergence theorems for rows of differential and algebraic .. (context) - BAKER, LUBINSKY - 1987
1 Elementarmathematik vom hoheren Standpunkt aus (context) - KLEIN - 1924
1 Grundlagen fur eine Theorie des jakobischen Kettenbruchalgor.. (context) - PERRON - 1907
1 Its Theory and Application (context) - BERNSTEIN, Algorithm - 1971
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