Program for calculating the integer order of Bessel functions with complex arguments

REN Hong-hong; GUO Ying-chun; WANG Bing-bing

doi:10.3969/j.issn.1000-5641.2019.01.009

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REN Hong-hong, GUO Ying-chun, WANG Bing-bing. Program for calculating the integer order of Bessel functions with complex arguments[J]. Journal of East China Normal University (Natural Sciences), 2019, (1): 76-82, 92. doi: 10.3969/j.issn.1000-5641.2019.01.009

Citation:

REN Hong-hong, GUO Ying-chun, WANG Bing-bing. Program for calculating the integer order of Bessel functions with complex arguments[J]. Journal of East China Normal University (Natural Sciences), 2019, (1): 76-82, 92. doi: 10.3969/j.issn.1000-5641.2019.01.009

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Program for calculating the integer order of Bessel functions with complex arguments

doi: 10.3969/j.issn.1000-5641.2019.01.009

1.
School of Physics and Materials Science, East China Normal University, Shanghai 200241, China
2.
Laboratory of Optical Physics, Beijing National Laboratory of Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

Received Date: 2017-12-20
Publish Date: 2019-01-25

Abstract

Abstract

Fortran source code for calculating the integer order of Bessel functions of the first kind with complex arguments is presented. The method is based on the backward recurrence relation of Bessel functions. Values of the Bessel function generated by our program are in-agreement with the values generated by Matlab to at least 12 significant digits. We use the program to calculate the integer order of Bessel functions of the first kind with pure imaginary arguments, provided by Xu Shiliang's Fortran algorithm assembly. The results show that the first 6 significant digits are accurate. We also analyze the algorithm for calculating Bessel functions with complex arguments, which use the infinite sum of the product of the real arguments of the Bessel function and the pure imaginary arguments of the Bessel function, provided by Xu Shiliang's algorithm assembly. The results show that this algorithm does not always get accurate values for Bessel functions with complex arguments. The reason lies with the fact that the term in the sum larger than the function value causes the loss of significant digits.
- Bessel function with complex arguments,
- Fortran source code,
- backward recurrence relation of Bessel function

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References

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