, Volume 39, Issue 3, pp 271–279 | Cite as

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

  • G. Allasia
  • R. Besenghi
Short Communication


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.

AMS Subject Classifications

65B15 65D20 65D30 

Key words

Triconi's psi function trapezoidal rule 

Numerische Berechnung von Tricomis Psi-Funktion mit der Trapezregel


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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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • G. Allasia
    • 1
  • R. Besenghi
    • 1
  1. 1.Dipartimento di MatematicaUniversità di TorinoTorinoItaly

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