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

Andrew R Booker, Andreas Strömbergsson, Holger L Then

Research output: Contribution to journal › Article (Academic Journal)

2 Citations (Scopus)
224 Downloads (Pure)

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 .
Original languageEnglish
Pages (from-to)78-108
Number of pages31
JournalLMS Journal of Computation and Mathematics
Volume16
Early online date10 Apr 2013
DOIs
Publication statusPublished - 2013

Keywords

  • Bessel function

Access to Document

  • Full-text PDF (accepted author manuscript)

    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, 454 KB

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    • Projects

    Explicit number theory, automorphic forms and L-functions

    Booker, A. R.

    1/10/09 → 1/04/15

    Project: Research

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