Ukrainian Mathematical Journal

, Volume 65, Issue 10, pp 1460–1478 | Cite as

Two-Dimensional Generalized Moment Representations and Padé Approximations for Some Humbert Series

  • A. P. Holub
  • L. O. Chernets’ka

By extending Dzyadyk’s method of generalized moment representations to the case of two-dimensional number sequences, we construct and study Padé approximants for some confluent Humbert hypergeometric series.


Power Series Bilinear Form Russian Translation Rational Approximation Formal Power Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. K. Dzyadyk, “On the generalization of the problem of moments,” Dop. Akad. Nauk URSR, 6, 8–12 (1981).MathSciNetGoogle Scholar
  2. 2.
    A. P. Holub and L. O. Chernets’ka, “Two-dimensional generalized model representations and rational approximations of functions of two variables,” Ukr. Mat. Zh., 65, No. 8, 1035–1058 (2013).MathSciNetGoogle Scholar
  3. 3.
    W. Rudin, Functional Analysis [Russian translation], Nauka, Moscow (1975).Google Scholar
  4. 4.
    A. P. Holub, Generalized Moment Representations and Padé Approximations [in Ukrainian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (2002).Google Scholar
  5. 5.
    P. Humbert, “Sur les fonctions hypercylindriques,” Comptes Rendus, 171, 490–492 (1920).zbMATHGoogle Scholar
  6. 6.
    H. Bateman and A. Erdélyi, Higher Transcendental Functions [Russian translation], Vol. 1, Nauka, Moscow (1973).Google Scholar
  7. 7.
    M. Abramowitz and I. A. Stegun (editors), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables [Russian translation], Nauka, Moscow (1979).Google Scholar
  8. 8.
    A. I. Markushevich, Theory of Analytic Functions [in Russian], Vol. 1, Nauka, Moscow (1967).Google Scholar
  9. 9.
    Y. L. Luke, Mathematical Functions and Their Approximations [Russian translation], Mir, Moscow (1980).Google Scholar
  10. 10.
    A. Cuyt, Padé Approximants for Operators: Theory and Applications, Springer, Berlin (1984).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • A. P. Holub
    • 1
  • L. O. Chernets’ka
    • 1
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine

Personalised recommendations