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Izv. Vyssh. Uchebn. Zaved. Mat., 2014, Number 9, Pages 59–68 (Mi ivm8930)  

This article is cited in 7 scientific papers (total in 7 papers)

On asymptotic form of the Hermite–Pade approximations for a system of Mittag-Leffler functions

A. P. Starovoitov

Chair of Differential Equations and Function Theory, F. Skorina Gomel State University, 104 Sovetskaya str., Gomel, 246019 Republic of Belarus

Abstract: Using the Laplace method we study asymptotic properties of Hermite integrals. In particular, we determine the asymptotic form of diagonal Hermite–Pade approximations for the system of exponents. Similar results are proved for the system of confluent hypergeometric functions. The obtained theorems supplement the known results by F. Wielonnsky, A. I. Aptekarev and other authors.

Keywords: Hermite integrals, joint Pade approximations, Hermite–Pade approximations, asymptotic equalities.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:9, 49–56

UDC: 517.538
Received: 17.03.2013

Citation: A. P. Starovoitov, “On asymptotic form of the Hermite–Pade approximations for a system of Mittag-Leffler functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 9, 59–68; Russian Math. (Iz. VUZ), 58:9 (2014), 49–56

Citation in format AMSBIB
\Bibitem{Sta14}
\by A.~P.~Starovoitov
\paper On asymptotic form of the Hermite--Pade approximations for a~system of Mittag-Leffler functions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2014
\issue 9
\pages 59--68
\mathnet{http://mi.mathnet.ru/ivm8930}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2014
\vol 58
\issue 9
\pages 49--56
\crossref{https://doi.org/10.3103/S1066369X14090060}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84906273462}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Astafieva, A. P. Starovoitov, “Hermite-Padé approximation of exponential functions”, Sb. Math., 207:6 (2016), 769–791  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. 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  mathnet
    3. M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov, “Approksimatsii Ermita–Pade vyrozhdennykh gipergeometricheskikh funktsii”, PFMT, 2017, no. 2(31), 69–74  mathnet
    4. A. P. Starovoitov, “Asymptotics of Diagonal Hermite–Padé Polynomials for the Collection of Exponential Functions”, Math. Notes, 102:2 (2017), 277–288  mathnet  crossref  crossref  mathscinet  isi  elib
    5. 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  mathnet  crossref  crossref  isi  elib
    6. A. P. Starovoitov, M. V. Sidortsov, A. A. Drapeza, “Skorost skhodimosti kvadratichnykh approksimatsii Ermita–Pade vyrozhdennykh gipergeometricheskikh funktsii”, PFMT, 2018, no. 1(34), 71–78  mathnet
    7. A. P. Starovoitov, “Hermite–Padé approximants of the Mittag-Leffler functions”, Proc. Steklov Inst. Math., 301 (2018), 228–244  mathnet  crossref  crossref  isi  elib  elib
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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