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Mat. Sb., 2007, Volume 198, Number 7, Pages 109–122 (Mi msb2662)  

This article is cited in 23 scientific papers (total in 23 papers)

Padé approximants of the Mittag-Leffler functions

A. P. Starovoitov*, N. A. Starovoitova

Francisk Skorina Gomel State University

Abstract: It is shown that for $m\le n$ the Padé approximants $\{\pi_{n,m}( \cdot ;F_{\gamma})\}$, which locally deliver the best rational approximations to the Mittag-Leffler functions $F_\gamma$, approximate the $F_\gamma$ as $n\to\infty$ uniformly on the compact set $D=ż:|z|\le1\}$ at a rate asymptotically equal to the best possible one. In particular, analogues of the well-known results of Braess and Trefethen relating to the approximation of $\exp{z}$ are proved for the Mittag-Leffler functions.
Bibliography: 28 titles.
* Author to whom correspondence should be addressed


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English version:
Sbornik: Mathematics, 2007, 198:7, 1011–1023

Bibliographic databases:

UDC: 517.51+517.53
MSC: 41A21, 33C05
Received: 08.08.2006 and 11.04.2007

Citation: A. P. Starovoitov, N. A. Starovoitova, “Padé approximants of the Mittag-Leffler functions”, Mat. Sb., 198:7 (2007), 109–122; Sb. Math., 198:7 (2007), 1011–1023

Citation in format AMSBIB
\by A.~P.~Starovoitov, N.~A.~Starovoitova
\paper Pad\'e approximants of the Mittag-Leffler functions
\jour Mat. Sb.
\yr 2007
\vol 198
\issue 7
\pages 109--122
\jour Sb. Math.
\yr 2007
\vol 198
\issue 7
\pages 1011--1023

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    This publication is cited in the following articles:
    1. A. P. Starovoitov, N. A. Starovoitova, “On the Asymptotics of the Rows of the Padé Table of Analytic Functions with Logarithmic Branch Points”, Math. Notes, 84:3 (2008), 379–388  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. S. P. Suetin, “Strong asymptotics of polynomials orthogonal with respect to a complex weight”, Sb. Math., 200:1 (2009), 77–93  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Yu. A. Labych, A. P. Starovoitov, “Trigonometric Padé approximants for functions with regularly decreasing Fourier coefficients”, Sb. Math., 200:7 (2009), 1051–1074  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Atkinson C., Osseiran A., “Rational solutions for the time-fractional diffusion equation”, SIAM J. Appl. Math., 71:1 (2011), 92–106  crossref  mathscinet  zmath  isi  scopus
    5. Atkinson C., Osseiran A., “Discrete-space time-fractional processes”, Fract. Calc. Appl. Anal., 14:2 (2011), 201–232  crossref  mathscinet  zmath  isi  scopus
    6. Yu. A. Labych, A. P. Starovoitov, “Priblizhenie nepreryvnykh funktsii ratsionalnymi drobyami Pade–Chebysheva”, PFMT, 2011, no. 1(6), 69–78  mathnet
    7. A. P. Starovoitov, “Approksimatsii Ermita–Pade dlya sistemy funktsii Mittag-Lefflera”, PFMT, 2013, no. 1(14), 81–87  mathnet
    8. A. P. Starovoitov, “On asymptotic form of the Hermite–Pade approximations for a system of Mittag-Leffler functions”, Russian Math. (Iz. VUZ), 58:9 (2014), 49–56  mathnet  crossref
    9. Francesco Mainardi, “On some properties of the Mittag-Leffler function $\mathbf{E_\alpha(-t^\alpha)}$, completely monotone for $\mathbf{t> 0}$ with $\mathbf{0<\alpha<1}$”, DCDS-B, 19:7 (2014), 2267  crossref  mathscinet  zmath  scopus
    10. M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov, “Approksimatsii Ermita–Pade vyrozhdennykh gipergeometricheskikh funktsii”, PFMT, 2017, no. 2(31), 69–74  mathnet
    11. 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
    12. 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
    13. Iyiola O.S., Asante-Asamani E.O., Wade B.A., “a Real Distinct Poles Rational Approximation of Generalized Mittag-Leffler Functions and Their Inverses: Applications to Fractional Calculus”, J. Comput. Appl. Math., 330 (2018), 307–317  crossref  mathscinet  zmath  isi  scopus
    14. 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
    15. A. P. Starovoitov, “Hermite–Padé approximants of the Mittag-Leffler functions”, Proc. Steklov Inst. Math., 301 (2018), 228–244  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    16. Taghavian H., “The Use of Partition Polynomial Series in Laplace Inversion of Composite Functions With Applications in Fractional Calculus”, Math. Meth. Appl. Sci., 42:7 (2019), 2169–2189  crossref  mathscinet  zmath  isi  scopus
    17. Gatheral J., Radoicic R., “Rational Approximation of the Rough Heston Solution”, Int. J. Theor. Appl. Financ., 22:3 (2019), 1950010  crossref  mathscinet  zmath  isi
    18. Sarumi I.O., Furati Kh.M., Khaliq A.Q.M., “Highly Accurate Global Pade Approximations of Generalized Mittag-Leffler Function and Its Inverse”, J. Sci. Comput., 82:2 (2020), UNSP 46  crossref  mathscinet  isi
    19. Jeng S.W., Kilicman A., “Fractional Riccati Equation and Its Applications to Rough Heston Model Using Numerical Methods”, Symmetry-Basel, 12:6 (2020), 959  crossref  isi
    20. Jeng S.W., Kilicman A., “Series Expansion and Fourth-Order Global Pade Approximation For a Rough Heston Solution”, Mathematics, 8:11 (2020), 1968  crossref  isi
    21. Starovoitov A.P. Kechko E.P., “Asymptotics For Hermite-Pade Approximants Associated With the Mittag-Leffler Functions”, Lobachevskii J. Math., 41:11, SI (2020), 2295–2302  crossref  mathscinet  isi
    22. N. V. Ryabchenko, A. P. Starovoitov, “Ratsionalnaya approksimatsiya funktsii Mittag–Lefflera”, PFMT, 2021, no. 1(46), 65–68  mathnet
    23. N. V. Ryabchenko, “Trigonometricheskie approksimatsii Pade spetsialnykh funktsii”, PFMT, 2021, no. 2(47), 81–83  mathnet
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