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PFMT, 2013, Issue 1(14), Pages 81–87 (Mi pfmt227)  

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.

Full text: PDF file (385 kB)
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Document Type: Article
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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    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:
    1. A. P. Starovoitov, “Asimptotika kvadratichnykh approksimatsii Ermita–Pade eksponentsialnykh funktsii”, PFMT, 2014, no. 1(18), 74–80  mathnet
    2. 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  mathnet
    3. A. V. Astafeva, “Asimptotika diagonalnykh approksimatsii Ermita–Pade dlya sistemy iz chetyrekh eksponent”, PFMT, 2015, no. 1(22), 53–57  mathnet
    4. 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
    5. 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
    6. M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov, “Approksimatsii Ermita–Pade vyrozhdennykh gipergeometricheskikh funktsii”, PFMT, 2017, no. 2(31), 69–74  mathnet
    7. 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
    8. 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
    9. 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  mathnet
    10. 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
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