An indirect method for evaluating certain infinite integrals

  • Arnold D. Kerr
Original Papers


This paper introduces a new approach for evaluating exactly certain infinite integrals. The method is demonstrated on a number of integrals which are not listed in the standard integral tables. The evaluated integrals are of the type
$$\int_0^\infty {kei (\lambda \eta ) d\eta ;} \int_{ - \infty }^\infty {kei (\lambda \sqrt {x^2 + \eta ^2 } ) d\eta ;} \int_{ - \infty }^\infty {sin (\alpha \eta ) kei|\lambda (y - \eta )|d\eta }$$
where kei is a modified Bessel function. It is also shown how other integrals of this type may be easily evaluated by the presented method.


Die Arbeit führt eine neue Methode zur genauen Auswertung gewisser unendlicher Integrale ein Diese Methode wird an einer Anzahl nicht in den gängigen Integraltafeln enthaltenen Integralen demonstriert. Die ausgewerteten Integrale sind vom Typ
$$\int_0^\infty {kei (\lambda \eta ) d\eta ;} \int_{ - \infty }^\infty {kei (\lambda \sqrt {x^2 + \eta ^2 } ) d\eta ;} \int_{ - \infty }^\infty {sin (\alpha \eta ) kei|\lambda (y - \eta )|d\eta }$$
(kei=modifizierte Besselfunktion). Es wird gezeigt wie auch andere Integrale dieses Typs durch die gezeigte Methode leicht erhalten werden können.


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Copyright information

© Birkhäuser Verlag 1978

Authors and Affiliations

  • Arnold D. Kerr
    • 1
  1. 1.Dept. of Civil EngineeringPrinceton UniversityPrincetonUSA

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