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This article is cited in 10 scientific papers (total in 10 papers)
MATHEMATICS
Hermite–Pade approximants of the system Mittag-Leffler functions
A. P. Starovoitov
F. Scorina Gomel State University, Gomel
Abstract:
The paper deals with asymptotic properties of Hermite integrals. In particular, the asymptotics of diagonal Hermite–Pade approximations $\pi^j_{kn,kn}(z;e^{j\xi})$ for the system of exponents $\{e^{jz}\}_{j=1}^k$ are determined when $j=1,2,…,k$ and $n\to\infty$. Similar results are proved for the system of confluent hypergeometric functions $\{_1F_1(1;\gamma;jz)\}_{j=1}^k$.
Keywords:
Hermite integrals, joint Pade approximations, Hermite–Pade approximations, asymptotic equality.
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UDC:
517.538.52+517.538.53
Received: 23.01.2013
Citation:
A. P. Starovoitov, “Hermite–Pade approximants of the system Mittag-Leffler functions”, PFMT, 2013, no. 1(14), 81–87
Citation in format AMSBIB
\Bibitem{Sta13}
\by A.~P.~Starovoitov
\paper Hermite--Pade approximants of the system Mittag-Leffler functions
\jour PFMT
\yr 2013
\issue 1(14)
\pages 81--87
\mathnet{http://mi.mathnet.ru/pfmt227}
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http://mi.mathnet.ru/eng/pfmt227 http://mi.mathnet.ru/eng/pfmt/y2013/i1/p81
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
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A. P. Starovoitov, “Asimptotika kvadratichnykh approksimatsii Ermita–Pade eksponentsialnykh funktsii”, PFMT, 2014, no. 1(18), 74–80
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A. P. Starovoitov, “Kvadratichnye approksimatsii Ermita–Pade eksponentsialnykh funktsii”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:4(1) (2014), 387–395
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A. V. Astafeva, “Asimptotika diagonalnykh approksimatsii Ermita–Pade dlya sistemy iz chetyrekh eksponent”, PFMT, 2015, no. 1(22), 53–57
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A. V. Astafieva, A. P. Starovoitov, “Hermite-Padé approximation of exponential functions”, Sb. Math., 207:6 (2016), 769–791
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M. V. Sidortsov, N. A. Starovoitova, A. P. Starovoitov, “Ob asimptotike approksimatsii Ermita–Pade vtorogo roda dlya eksponentsialnykh funktsii s kompleksnymi mnozhitelyami v pokazatelyakh eksponent”, PFMT, 2017, no. 1(30), 73–77
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M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov, “Approksimatsii Ermita–Pade vyrozhdennykh gipergeometricheskikh funktsii”, PFMT, 2017, no. 2(31), 69–74
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A. P. Starovoitov, “Asymptotics of Diagonal Hermite–Padé Polynomials for the Collection of Exponential Functions”, Math. Notes, 102:2 (2017), 277–288
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A. P. Starovoitov, E. P. Kechko, “On Some Properties of Hermite–Padé Approximants to an Exponential System”, Proc. Steklov Inst. Math., 298 (2017), 317–333
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M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov, “Skorost skhodimosti kvadratichnykh approksimatsii Ermita–Pade vyrozhdennykh gipergeometricheskikh funktsii”, PFMT, 2018, no. 1(34), 71–78
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A. P. Starovoitov, “Hermite–Padé approximants of the Mittag-Leffler functions”, Proc. Steklov Inst. Math., 301 (2018), 228–244
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