Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T15:22:35.661Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Bessel function $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}J_\nu (x)$ in the transition region

Part of: Approximations and expansions

Published online by Cambridge University Press:  01 June 2014

Ilia Krasikov
Ilia Krasikov*
Affiliation:
Department of Mathematical Sciences, Brunel University, Uxbridge UB8 3PH, United Kingdom email mastiik@brunel.ac.uk

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give an approximation for the value of the Bessel function $J_\nu (x)$ in the transition region with an explicit sharp error term.

MSC classification

Secondary: 33C10: Bessel and Airy functions, cylinder functions, $_0F_1$ 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Issue 1 , 2014 , pp. 273 - 281
Copyright
© The Author 2014 

References

Elbert, Á. and Laforgia, A., ‘A lower bound for J ν (ν)’, Appl. Anal. 19 (1985) 137–145.Google Scholar
Finch, S., ‘Bessel function zeroes’, Mathematical constants (supplementary material) (Cambridge University Press, Cambridge, 2003).Google Scholar
Krasikov, I., ‘Approximations for the Bessel and Airy functions with an explicit error term’, LMS J. Comput. Math. to appear.Google Scholar
Olver, F. W. J., Lozier, D. W., Boisvert, R. F. and Clark, C. W. (eds), NIST handbook of mathematical functions (Cambridge University Press, Cambridge, 2010).Google Scholar
Qu, C. K. and Wong, R., ‘“Best possible” upper and lower bounds for the zeros of the Bessel function J ν (x)’, Trans. Amer. Math. Soc. 351 (1999) 2833–2859.CrossRefGoogle Scholar
Szegö, G., Orthogonal polynomials , Colloquium Publications 23 (American Mathematical Society, Providence, RI, 1975).Google Scholar