Communications in Mathematical Sciences

Volume 15 (2017)

Number 7

Approximate linear relations for Bessel functions

Pages: 1967 – 1986



Gang Pang (Department of Mechanics, College of Engineering, Peking University, Beijing, China)

Shaoqiang Tang (HEDPS, CAPT and LTCS, College of Engineering, Peking University, Beijing, China)


In this study, we reveal an approximate linear relation for Bessel functions of the first kind, based on asymptotic analyses. A set of coefficients are calculated from a linear algebraic system. For any given error tolerance, a Bessel function of an order big enough is approximated by a linear combination of those with neighboring orders using these coefficients. This naturally leads to a class of ALmost EXact (ALEX) boundary conditions in atomic and multiscale simulations.


Bessel function, asymptotic analysis, approximate linear relation, ALEX boundary condition

2010 Mathematics Subject Classification

33C10, 41A60

This study is partially supported by the National Natural Science Foundation of China under contract numbers 11521202, 11502028 and 11272009.

Received 30 April 2016

Accepted 1 July 2017

Published 16 October 2017