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On a Gaussian Quadrature Formula for Entire Functions of Exponential Type

  • Chapter
Numerical Methods of Approximation Theory/Numerische Methoden der Approximationstheorie

Abstract

Given a system of n distinct points x1, x2,..., xn let

$$\begin{gathered} \omega (x)\quad :\prod\limits_{\upsilon = 1}^n {(x - {x_\upsilon })} \;and\;{\ell _\upsilon }(x)\;: = \frac{{\omega (x)}}{{\omega '({x_\upsilon })(x - {x_\upsilon })}} \hfill \\ (\upsilon = 1,2,...,n). \hfill \\ \end{gathered} $$

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References

  1. Boas, R.P., Jr. (1954) Entire functions (Academic Press, New York).

    Google Scholar 

  2. Boas, R.P., Jr. (1972) Summation formulas and bandlimited signals. Tôhoku Math. J. 24, 121–125.

    Article  Google Scholar 

  3. Carlson, F. (1914) Sur une classe de séries de Taylor (Thesis, Uppsala).

    Google Scholar 

  4. Frappier, C. and Q.I. Rahman (1986) Une formule de quadrature pour les fonctions entières de type exponentiel. Les Annales des Sciences Mathématiques du Québec 10, 17–26.

    Google Scholar 

  5. Hermite, Ch. (1878) Sur la formule d’interpolation de Lagrange. J. reine angew. Math. 84, 70–79.

    Article  Google Scholar 

  6. Olivier, P. and Q.I. Rahman (1986) Sur une formule de quadrature pour des fonctions entières. Modélisation mathématique et Analyse numérique 20, 517–537.

    Google Scholar 

  7. Szegö, G. (1967) Orthogonal polynomials, 3rd edn (Amer. Math. Soc., Providence, Rhode Island).

    Google Scholar 

  8. Titchmarsh, E.C. (1948) Introduction to the theory of Fourier integrals, 2nd edn (Oxford University Press, London).

    Google Scholar 

  9. Turán, P. (1950) On the theory of the mechanical quadrature. Acta Scient. Math. 12, 30–37.

    Google Scholar 

  10. Valiron, G. (1925) Sur la formule d’interpolation de Lagrange. Bull. Sci. Math. (2) 49, 181–192, 203-224.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Département de Mathématiques et de Statistique, Université de Montréal, P.Q., H3C 3J7, Canada

    Qazi Ibadur Rahman

  2. Mathematisches Institut, Universität Erlangen — Nürnberg, Bismarckstr. 1 1/2, D-8520, Erlangen, Federal Republic of Germany

    Gerhard Schmeisser

Authors
  1. Qazi Ibadur Rahman
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  2. Gerhard Schmeisser
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Editor information

Editors and Affiliations

  1. Hamburg, Germany

    Lothar Collatz

  2. Mannheim, Germany

    Günther Meinardus

  3. Erlangen-Nürnberg, Germany

    Günther Nürnberger

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© 1987 Springer Basel AG

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Rahman, Q.I., Schmeisser, G. (1987). On a Gaussian Quadrature Formula for Entire Functions of Exponential Type. In: Collatz, L., Meinardus, G., Nürnberger, G. (eds) Numerical Methods of Approximation Theory/Numerische Methoden der Approximationstheorie. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 81. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6656-9_14

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  • DOI: https://doi.org/10.1007/978-3-0348-6656-9_14

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-6657-6

  • Online ISBN: 978-3-0348-6656-9

  • eBook Packages: Springer Book Archive

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