Bill Allombert on Fri, 10 Feb 2012 15:26:44 +0100 |
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bessel function algorithm |
Hello PARI users, I forward this post from Marcel Bezerra about the Bessel function which was misfilled. From: Marcel Bezerra <gigamaxell@gmail.com> Date: Fri, 10 Feb 2012 11:38:57 -0200 Hello! I'm working with cylindrical electromagnetic waveguides. The conditions I'm studying now need solutions using Bessel functions with complex order. I need to calculate them numerically, so I started to look for software capable to calculate such functions. I need some info about the algorithms used to calculate bessel functions. I want to know what algorithm is used to calculate bessel functions with complex order and argument in PARI/GP. I found some papers regarding this subject. The first one is the Algorithm 644 from Amos. But his paper says his method is applied for nonnegative order. The second one is from Masao Kodama, that is exactly an algorithim about complex order and argument. I used a software called Mathematica, that showed in an example the bessel function of order 7.3 + 1.0*I and argument 4.5-1*I. But they don't make any reference about the algorithm they use. I found out the PARI/GP software also is capable to deal with complex order, and tested the same example and I got the same result compared to Mathematica. I need the info of the algorithm used in PARI to calculate bessel functions in order to know if there are any limitations of order, argument, precision and so on. Thank you in advance! Regards from Brazil! Marcel Bezerra