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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

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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

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