Asymptotic of Bessel function of complex argument
- From: roucaries dot bastien __at__ gmail dot com <roucaries.bastien@xxxxxxxxx>
- Date: Wed, 22 Aug 2007 09:17:24 -0700
Hi,
I am programming a bessel function of first kind of large argument (|
z| > 25, order < 8, computation done in the first quadran) using A&S
(9.2.5), (9.2.9), (9.2.10) .
I stop to add P & Q when pk+1 > Pk and Qk+1 > Qk.
However I get a really bad precision (on the order of 1e-2) comparing
my program with octave (AMOS).
Do you have any idea of this behavior? I have read* that some author
prefer to use A&S (9.2.19) because more reliable. What do you think?
Should I use more powerfull method like Paris** method?
I can send you a copy of my code by private mail if you want. (I plan
to release it under LGPL when it will work)
Regards
Bastien
* http://freespace.virgin.net/boost.regex/toolkit/html/math_toolkit/special/bessel/bessel.html
**@article{1016194,
author = {R. B. Paris},
title = {On the use of Hadamard expansions in hyperasymptotic
evaluation of Laplace-type integrals: II. complex variable},
journal = {J. Comput. Appl. Math.},
volume = {167},
number = {2},
year = {2004},
issn = {0377-0427},
pages = {321--343},
doi = {http://dx.doi.org/10.1016/j.cam.2003.10.021},
publisher = {Elsevier Science Publishers B. V.},
address = {Amsterdam, The Netherlands, The Netherlands},
}
@article{1016193,
author = {R. B. Paris},
title = {On the use of Hadamard expansions in hyperasymptotic
evaluation of Laplace-type integrals: I: real variable},
journal = {J. Comput. Appl. Math.},
volume = {167},
number = {2},
year = {2004},
issn = {0377-0427},
pages = {293--319},
doi = {http://dx.doi.org/10.1016/j.cam.2003.10.005},
publisher = {Elsevier Science Publishers B. V.},
address = {Amsterdam, The Netherlands, The Netherlands},
}
.
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