Analysis in Theory and Applications

, Volume 22, Issue 2, pp 105–113 | Cite as

(0,1;0)-Interpolation on infinite interval (−∞, +∞)

  • Pankaj Mathur


In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤3n −2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H n (x) and the first derivatives at the zeros of H n (x).

Key words

interpolation Hermite polynomials convergence 

AMS(2000) subject classification



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  1. [1]
    Balázs, J., Sulyozott (0,2)-interpolació Ultrazféricus Polimok Gyökein, MTA, 11(1961), 305–338.MATHGoogle Scholar
  2. [2]
    Eneduanya, S. A., On Convergence of Interpolation Polynomials, Analysis Maths., 11(1985), 13–22.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Freud, G., On Two Polynomial Ineqalities, Acta Math. Acad. Sci. Hungar., 22(1971), 109–116.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    —, On Polynomial Approximation with Weight exp(−x 2k/2), Acta Math. Acad. Sci. Hungar., 24(1973), 363–371.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    Joó, I., On Pál Interpolation, Annales Univ. Sci. Budapest, Sect. Math., 37(1994), 247–262.MATHGoogle Scholar
  6. [6]
    Pál, L.G., A General Lacunary (0; 0,1)-interpolation Process, Annales Univ. Budapest, Sect. Comp., 16(1996), 291–301.MATHGoogle Scholar
  7. [7]
    Pál, L.G., A New Modification to Hermite-Féjér Interpolation, Analysis Math., (1975), 197–205.Google Scholar
  8. [8]
    Sebestyén, Z.F., Pál Type Interpolation on the Roots of Hermite Polynomials, Pure Math. Appl., 9:3–4(1998),429–439.MathSciNetMATHGoogle Scholar
  9. [9]
    Srivastava, R. and Mathur, K.K., An Interpolation Process on the Roots of Hermite Polynomials (0;0,1) Interpolation on Infinite Interval, Bull. Ins. of Math Acad Sinica, Vol 26, No.3, Sep'1998.Google Scholar
  10. [10]
    Szegö, G., Orthogonal Polynomials, Amer. Math. Soc., Coll. Publ., New York, 1959.MATHGoogle Scholar
  11. [11]
    Szili, L., A Convergence Theorem for the Pál- method of Interpolation on the Roots of Hermite Polynomials, Analysis Math., 11(1985), 75–84.MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    Xie, T.F., On Páls Problem, Chinese Quart. J.Math. 7(1992), 48–52.MathSciNetMATHGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Pankaj Mathur
    • 1
  1. 1.Department of Mathematics and AstronomyLucknow UniversityLucknowIndia

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