Geodesic
Hermitian approximation of two exponents
Problemy fiziki, matematiki i tehniki, no. 1 (2012), pp. 97-100.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the asymptotic properties of diagonal Pade–Hermite approximants $\{\pi^{j}_{2n,2n}(z;e^{j\xi;})\}^{2}_{j=1}$ for a system consisting of functions $\{e^z,e^{2 z}\}$. In particular, we determine the asymptotic behavior of the differences $e^{jz} - \pi^j_{2n,2n}(z; e^{j\xi})$ for $j =1,2$ and $n \to\infty$ for any complex number $z$. The obtained results supplement research of Pade, Perron, Braess and A.I. Aptekarev dealing with the study of the convergence of joint Pade approximants for systems of exponents.
Keywords: perfect system of functions, asymptotic equality, Hermite integrals.
Mots-clés : joint Pade approximant, Pade–Hermite approximants 
@article{PFMT_2012_1_a17,
     author = {N. V. Rjabchenko and A. P. Starovoitov and G. N. Kazimirov},
     title = {Hermitian approximation of two exponents},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {97--100},
     publisher = {mathdoc},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2012_1_a17/}
}
TY  - JOUR
AU  - N. V. Rjabchenko
AU  - A. P. Starovoitov
AU  - G. N. Kazimirov
TI  - Hermitian approximation of two exponents
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2012
SP  - 97
EP  - 100
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2012_1_a17/
LA  - ru
ID  - PFMT_2012_1_a17
ER  - 
%0 Journal Article
%A N. V. Rjabchenko
%A A. P. Starovoitov
%A G. N. Kazimirov
%T Hermitian approximation of two exponents
%J Problemy fiziki, matematiki i tehniki
%D 2012
%P 97-100
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2012_1_a17/
%G ru
%F PFMT_2012_1_a17
N. V. Rjabchenko; A. P. Starovoitov; G. N. Kazimirov. Hermitian approximation of two exponents. Problemy fiziki, matematiki i tehniki, no. 1 (2012), pp. 97-100. http://geodesic.mathdoc.fr/item/PFMT_2012_1_a17/

[1] E. M. Nikishin, V. N. Sorokin, Ratsionalnye approksimatsii i ortogonalnost, Nauka, M., 1988 | MR | Zbl

[2] Dzh. Beiker ml., P. Greivs-Morris, Approksimatsii Pade, Mir, M., 1986 | MR

[3] K. Mahler, “Perfect systems”, Compositio mathematica, 19:2 (1968), 95–166 | MR | Zbl

[4] N. A. Jager, “Multidimensional Generalization of the Pade Table”, K. Nederl. Ak. Wetensch., Ser. A, 67 (1964), 192–249

[5] J. Coates, “On the algebraic approximation of functions”, K. Nederl. Ak. Wetensch., Ser. A, 69 (1966), 421–461 | MR | Zbl

[6] E. M. Nikishin, “O sisteme markovskikh funktsii”, Vestn. MGU. Seriya 1. Matematika. Mekhanika, 1979, no. 4, 60–63 | MR | Zbl

[7] A. I. Aptekarev, V. G. Lysov, “Sistemy markovskikh funktsii, generiruemye grafami, i asimptotika ikh approksimatsii Ermita–Pade”, Matem. sbornik, 201:2 (2010), 29–78 | DOI | MR | Zbl

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

[9] F. Klein, Elementarnaya matematika s tochki zreniya vysshei, v. 1, Nauka, M., 1933

[10] A. I. Aptekarev, “O skhodimosti ratsionalnykh approksimatsii k naboru eksponent”, Vestnik MGU. Seriya 1. Matematika. Mekhanika, 1981, no. 1, 68–74 | MR | Zbl

[11] H. Pade, “Memoire sur les developpement en fractions continues de la fonction exponential”, Ann Sci., Ecole Normale Sup. (3), 16 (1899), 394–426 | MR

[12] O. Perron, Die Lehre von den Kettenbrüchen, Teubner, Leipzig–Berlin, 1929 | Zbl

[13] D. Braess, “On the conjecture of Meinardus on rational approximation of $e^x$, II”, J. Approx. Theory, 40:4 (1984), 375–379 | DOI | MR | Zbl

[14] P. P. Petrusherv, V. A. Popov, Rational approximation of real function, Encyclopedia Math., Cambridge, 1987