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Numerical computation of Tricomi's psi function by the trapezoidal rule

Numerische Berechnung von Tricomis Psi-Funktion mit der Trapezregel

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Abstract

The trapezoidal rule is applied to the numerical calculation of an integral representation of Tricomi's psi function Ψ(a, c; x) fora, x ε ℝ+ andc ε ℝ. The unexpectedly high accuracy is explained by means of a careful investigation of the remainder terms of the Euler-Maclaurin formula. A simple and efficient numerical procedure for obtaining values of the psi function is given.

Zusammenfassung

Die Trapezregel wird zur numerischen Auswertung einer Integraldarstellung von Tricomis Psi-Funktion Ψ(a, c; x) füra, x ε ℝ+ undc ε ℝ verwendet. Die unvermutet hohe Genauigkeit wird durch eine gründliche Untersuchung des Restglieds der Euler-Maclaurin-Formel erklärt. Außerdem wird eine einfache und effektive numerische Prozedur angegeben, durch die man explizite Zahlenwerte der Psi-Funktion erhält.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, I-10123, Torino, Italy

    G. Allasia &  R. Besenghi

Authors
  1. G. Allasia
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  2. R. Besenghi
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Additional information

This work has been supported by the Ministero della Pubblica Istruzione and the Consiglio Nazionale delle Ricerche.

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Allasia, G., Besenghi, R. Numerical computation of Tricomi's psi function by the trapezoidal rule. Computing 39, 271–279 (1987). https://doi.org/10.1007/BF02309560

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  • DOI: https://doi.org/10.1007/BF02309560

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