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Multipoint Padé approximations of the beta function

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Abstract

We study multipoint rational approximations with free poles for the beta function. The denominators of the approximations satisfy orthogonality relations with variable weight with respect to a discrete measure. We obtain the limit distribution of the zeros of the denominators. A potential-theoretic interpretation of the results obtained is given.

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References

  1. E.M. Nikishin and V. N. Sorokin, Rational Approximations and Orthogonality (Nauka, Moscow, 1988) [in Russian].

    MATH  Google Scholar 

  2. A. A. Gonchar and G. Lopez-Lagomasino, “Markov’s theorem for multipoint Padé approximants,” Mat. Sb. 105(4), 512–524 (1978).

    MathSciNet  Google Scholar 

  3. A. A. Gonchar and E. A. Rakhmanov, “Equilibrium distributions and rate of rational approximation of analytic functions,” Mat. Sb. 134(3), 306–352 (1987).

    Google Scholar 

  4. A. I. Aptekarev, “Sharp constants for rational approximations of analytic functions,” Mat. Sb. 193(1), 3–72 (2002) [Russian Acad. Sci. Sb. Math. 193 (1), 1–72 (2002)].

    MathSciNet  Google Scholar 

  5. E. A. Rakhmanov, “Equilibrium measure and the distribution of zeros of the extremal polynomials of a discrete variable,” Mat. Sb. 187(8), 109–124 (1996) [Russian Acad. Sci. Sb. Math. 187 (8), 1213–1228 (1996)].

    MathSciNet  Google Scholar 

  6. G. Szegö, Orthogonal Polynomials in Colloquium Publ. (Amer. Math. Soc., Providence, RI, 1959; Fizmatgiz, Moscow, 1962), Vol. XXIII.

    Google Scholar 

  7. P. D. Dragnev and E. B. Saff, “Constrained energy problems with applications to orthogonal polynomials of a discrete variable,” J. Anal. Math. 72, 223–259 (1997).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. A. Kandayan

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  1. A. A. Kandayan
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Correspondence to A. A. Kandayan.

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Original Russian Text © A. A. Kandayan, 2009, published in Matematicheskie Zametki, 2009, Vol. 85, No. 2, pp. 189–203.

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Kandayan, A.A. Multipoint Padé approximations of the beta function. Math Notes 85, 176–189 (2009). https://doi.org/10.1134/S0001434609010210

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  • DOI: https://doi.org/10.1134/S0001434609010210

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