Skip to content

Bounds and algorithms for the K-Bessel function of imaginary order

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)78-108
Number of pages31
JournalLMS Journal of Computation and Mathematics
Volume16
Early online date10 Apr 2013
DOIs
DateAccepted/In press - 2 Oct 2012
DateE-pub ahead of print - 10 Apr 2013
DatePublished (current) - 2013

Abstract

Using the paths of steepest descent, we prove precise bounds with numerical implied constants for the modified Bessel function of imaginary order and its first two derivatives with respect to the order. We also prove precise asymptotic bounds on more general (mixed) derivatives without working out numerical implied constants. Moreover, we present an absolutely and rapidly convergent series for the computation of and its derivatives, as well as a formula based on Fourier interpolation for computing with many values of . Finally, we have implemented a subset of these features in a software library for fast and rigorous computation of .

    Research areas

  • Bessel function

Download statistics

No data available

Documents

Documents

  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Cambridge University Press at https://www.cambridge.org/core/journals/lms-journal-of-computation-and-mathematics/article/bounds-and-algorithms-for-the-kbessel-function-of-imaginary-order/AB68D056F1A8398C9E06C61E2D94529A. Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 453 KB, PDF-document

DOI

View research connections

Related faculties, schools or groups