Abstract
In the present paper, results on the strong asymptotics of row sequences \(\{\pi _{n,m}\},\,n\rightarrow \infty ,\, m\)-fixed of classical Padé approximants are provided.
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References
Blatt, H.P., Kovacheva, R.K.: Growth behavior and zero distribution of rational functions. Constr. Approx. 34(3), 393–420 (2011)
Blatt, H.P., Grothmann, R., Kovacheva, R.K.: Regions of meromorphy and value distribution of geometrically converging rational approximants. J. Math. Anal. Appl. 382, 66–76 (2011)
Blatt, H.P., Saff, E.B., Simkani, M.: Jentzsch-Szegö type theorems for the zeros of best approximants. J. Lond. Math. Soc. 38, 307–316 (1988)
Buslaev, V.I.: Relations for the coefficients, and singular points of a function. Mat. Sb. 131(173), 357–384 (1986) [English transl. in Math. USSR Sb. 59 (1988)]
Cacoq, J., de la Calle Ysern, B., López Lagomasino, G.: Direct and inverse results on row sequences of Hermite-Paé approximants. Constr. Approx. 38, 133–160 (2013)
de Montessus de Ballore, R.: Sur le fractions continues algebriques. Bull. Soc. Math. France 30, 28–36 (1902)
Gonchar, A.A.: Poles of the rows of the Padé table and meromorphic continuation of functions. Mat. Sb. 115(157), 590–615 (1981) [English transl. in Math. USSR Sb. 43 (1982)]
Gonchar, A.A.: On the speed of rational approximation of some analytic functions. Mat. Sb. (NS) 105, 147–163 (1978) [English transl. in Math. USSR Sb 34 (1978)]
Hernándes, B., De la Calli Ysern, B.: Meromorphic continuation of functions and arbitrary distribution of interpolation points. J. Math. Anal. Appl. 403, 107–119 (2013)
Kakehashi, T.: The decomposition of coefficients of power series and the divergence of the interpolating polynomials. Proc. Jpn. Acad. 31(8), 517–523 (1955)
Kakehashi, T.: On interpolation of analytic functions. II. Fundamental results. Proc. Jpn. Acad. 32, 713–718 (1956)
Khristoforov, D.N.: On the asymptotic properties of interpolating polynomials. Matem. zametki t.83(1), 129–138 (2008) [English transl. in Math. Notes 83(1), 116–124 (2008)]
Kovacheva, R.K.: Generalized Padé approximants and meromorphic continuation of functions. Mat. Sb 109 (1979) [English transl. Math. USSR Sb. 37, 337–348 (1980)]
Landkoff, N.I.: Foundations of Modern Potential Theory, Grundlehren der mathematischen Wissenschaften. Springer, Berlin (1972)
Perron, O.: Die Lehre von den Kettenbrüchen, Vol. II, 3rd ed. Teubner Verlag, Stuttgart (1957)
Saff, E.B.: An extension of Montessus de Ballores theorem on the convergence of interpolating rational functions. J. Approx. Theory 6, 63–67 (1972)
Saff, E.B., Totik, V.: Logarithmic Potentials with External Fields. Springer, Heidelberg (1997)
Suetin, S.P.: On the poles of the mth row of the Padé table. Mat. Sb. 120(162), 500–504 (1983) [English transl. in Math. USSR Sb. 48 (1984)]
Suetin, S.P.: On an inverse problem for the mth row of the Padé table. Mat. Sb. 124(166), 238–251 (1984) [English transl. in Math. USSR Sb. 52 (1985)]
Vavilov, V.V., López, G., Prokhorov, V.A.: On an inverse problem for the rows of the Padé table. Mat. Sb. 110(152), 117–129 (1979) [English transl. in Math. USSR. 38 (1981)]
Walsh, J.L.: Overconvergence, degree of convergence and zeros of sequences of analytic functions. Duke Math. 13, 195–234 (1946)
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Kovacheva, R.K. (2018). On the Strong Asymptotics of Rows of the Padé Table. In: Georgiev, K., Todorov, M., Georgiev, I. (eds) Advanced Computing in Industrial Mathematics. Studies in Computational Intelligence, vol 728. Springer, Cham. https://doi.org/10.1007/978-3-319-65530-7_10
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DOI: https://doi.org/10.1007/978-3-319-65530-7_10
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