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On summation formulas due to Plana, Lindelöf and Abel, and related Gauss-christoffel rules, I

  • Germund Dahlquist
Article

Abstract

Three methods, old but not so well known, transform an infinite series into a complex integral over an infinite interval. Gauss quadrature rules are designed for each of them. Various questions concerning their construction and application are studied, theoretically or experimentally. They are so efficient that they should be considered for the development of software for special functions.

Applications are made to slowly convergent alternating and positive series, to Fourier series, to the numerical analytic continuation of power series outside the circle of convergence, and to ill-conditioned power series.

AMS subject classification

65B10 65D30 65E05 33A65 40A15 65F15 

Key words

Convergence acceleration analytic continuation ill-conditioned series Gauss quadrature orthogonal polynomials infinite interval experimental mathematics 

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Copyright information

© BIT Foundaton 1997

Authors and Affiliations

  • Germund Dahlquist
    • 1
  1. 1.NADARoyal Institute of TechnologyStockholmSweden

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