Asymptotics of diagonal Hermite--Pade approximants for a system of four exponentials
Problemy fiziki, matematiki i tehniki, no. 1 (2015), pp. 53-57.

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Asymptotic properties of diagonal Hermite–Pade approximants of type I for exponential system $\{e^{\lambda_jz}\}^3_{j=0}$ with arbitrary real $\lambda_0\lambda_1\lambda_2\lambda_3$ are studied. The obtained theorems complement the results of P. Borwein and F. Wielonsky.
Mots-clés : Hermite–Pade approximants of type I
Keywords: asymptotic equality, saddle-point method.
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A. V. Astafyeva. Asymptotics of diagonal Hermite--Pade approximants for a system of four exponentials. Problemy fiziki, matematiki i tehniki, no. 1 (2015), pp. 53-57. http://geodesic.mathdoc.fr/item/PFMT_2015_1_a9/

[1] C. Hermite, “Sur la generalisation des fractions continues algebriques”, Ann. Math. Pura. Appl. Ser. 2A, 21 (1883), 289–308

[2] C. Hermite, “Sur la fonction exponentielle”, C. R. Akad. Sci. (Paris), 77 (1873), 18–293

[3] K. Mahler, “Perfect systems”, Comp. Math., 19 (1968), 95–166

[4] K. Mahler, “Zur Approximation der Exponential funktion und des Logarithmus. I; II”, J. Reine Angew. Math., 166 (1931), 118–150

[5] A. I. Aptekarev, H. Stahl, “Asymptotics of Hermite–Pade polynomials”, Progress in Approximation Theory, eds. A. A. Gonchar, E. B. Saff, Springer-Verlag, New York–Berlin, 1992, 127–167 | DOI

[6] A. I. Aptekarev, V. I. Buslaev, A. Martines-Finkelshtein, S. P. Suetin, “Approksimatsii Pade, nepreryvnye drobi i ortogonalnye mnogochleny”, Uspekhi matem. nauk, 66:6(402) (2011), 37–122 | DOI

[7] K. Mahler, “Applications of some formulas by Hermite to the approximation of exponentials and logarithms”, Math. Ann., 1668 (1967), 200–227 | DOI

[8] G. V. Chudnovsky, “Hermite–Pade approximations to exponential functions and elementary estimates of the measure of irrationality of”, Lecture Notes in Math., 925, Springer-Verlag, New York–Berlin, 1982, 299–322 | DOI

[9] H. Pade, “Memoire sur les developpements en fractions continues de la fonctial exponential”, Ann. Ecole Norm. Sup. Paris, 16:3 (1899), 394–426

[10] P. B. Borwein, “Quadratic Hermite–Pade approximation to the exponential function”, Const. Approx., 62 (1986), 291–302 | DOI

[11] F. Wielonsky, “Asymptotics of Diagonal Hermite–Pade Approximants to”, J. Approx. Theory, 90:2 (1997), 283–298 | DOI

[12] A. P. Starovoitov, “Approksimatsii Ermita–Pade dlya sistemy funktsii Mittag–Lefflera”, Problemy fiziki, matematiki i tekhniki, 2013, no. 1(14), 81–87

[13] K. A. Driver, “Non-diagonal quadratic Hermite–Pade approximation to the exponential function”, J. Comp. Appl. Math., 65 (1995), 125–134 | DOI

[14] Yu. V. Sidorov, M. V. Fedoryuk, M. I. Shabunin, Lektsii po teorii funktsii kompleksnogo peremennogo, Nauka, M., 1989

[15] A. I. Markushevich, Teoriya analiticheskikh funktsii, v. 1, Nauka, M., 1967