On summation formulas due to Plana, Lindelöf and Abel, and related Gauss-Christoffel rules. II

DOI10.1007/BF02510353zbMath0893.65001OpenAlexW4239027912MaRDI QIDQ1378462

Germund Dahlquist

Publication date: 24 August 1998

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02510353

zbMATH Keywords

numerical resultsorthogonal polynomialsthree-term recurrence relationnumerical testGauss-Lindelöf formulaLindelöf's summation formula

Mathematics Subject Classification ID

General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Numerical summation of series (65B10)

Related Items (5)

Construction of Gaussian quadrature formulas for even weight functions ⋮ Summation Formulas of Euler–Maclaurin and Abel–Plana: Old and New Results and Applications ⋮ Quadrature processes for efficient calculation of the Clausen functions ⋮ Binet-type polynomials and their zeros ⋮ Nonstandard Gaussian quadrature formulae based on operator values

Cites Work

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• Bernoulli and Euler numbers and orthogonal polynomials
• Convergence acceleration on a general class of power series
• Numerical Calculation of Certain Definite Integrals by Poisson's Summation Formula
• Pi, Euler Numbers, and Asymptotic Expansions
• Convergence acceleration from the point of view of linear programming

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