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

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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.

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References

  1. V. K. Dzyadyk, “On the generalization of the problem of moments,” Dop. Akad. Nauk URSR, 6, 8–12 (1981).

    MathSciNet  Google Scholar 

  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).

    MathSciNet  Google Scholar 

  3. W. Rudin, Functional Analysis [Russian translation], Nauka, Moscow (1975).

    Google Scholar 

  4. A. P. Holub, Generalized Moment Representations and Padé Approximations [in Ukrainian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (2002).

  5. P. Humbert, “Sur les fonctions hypercylindriques,” Comptes Rendus, 171, 490–492 (1920).

    MATH  Google Scholar 

  6. H. Bateman and A. Erdélyi, Higher Transcendental Functions [Russian translation], Vol. 1, Nauka, Moscow (1973).

    Google Scholar 

  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. A. I. Markushevich, Theory of Analytic Functions [in Russian], Vol. 1, Nauka, Moscow (1967).

    Google Scholar 

  9. Y. L. Luke, Mathematical Functions and Their Approximations [Russian translation], Mir, Moscow (1980).

    Google Scholar 

  10. A. Cuyt, Padé Approximants for Operators: Theory and Applications, Springer, Berlin (1984).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    A. P. Holub & L. O. Chernets’ka

Authors
  1. A. P. Holub
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  2. L. O. Chernets’ka
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Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 10, pp. 1315–1331, October, 2013.

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Holub, A.P., Chernets’ka, L.O. Two-Dimensional Generalized Moment Representations and Padé Approximations for Some Humbert Series. Ukr Math J 65, 1460–1478 (2014). https://doi.org/10.1007/s11253-014-0872-4

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  • DOI: https://doi.org/10.1007/s11253-014-0872-4

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