I want to implement the Bessel functions of first and second kindDescription of bessel functions for complex numbers in C++. Now I am looking for possibilities to introduce them in my source code. Since math.h only contains bessel functions for real numbers, I would be interested in seeing any kind of possibility.
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`http://www.catb.org/esr/faqs/smart-questions.html` – gifnoc-gkp Aug 03 '13 at 19:15
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what are Bessel functions?! – Minimus Heximus Aug 03 '13 at 19:15
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Can you implement them with real numbers? – Minimus Heximus Aug 03 '13 at 19:19
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No, but math.h has them. you get them with jn(unsigned int, double x) and yn(unsigned int, double x) – Aug 03 '13 at 19:20
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So you may need a function which describes complex Bessel function in terms of real bessel or other funcions. Can you describe the function in this way? – Minimus Heximus Aug 03 '13 at 19:23
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Although your first sentence sounds right, I do not understand your question. – Aug 03 '13 at 19:25
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suppose f(x+iy) is the compex bessel function. Can you find real functions g(x,y) and h(x,y) with f(x+iy)=g(x,y)+ih(x,y)? – Minimus Heximus Aug 03 '13 at 19:28
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if I could, then I had solved my problem.. – Aug 03 '13 at 19:30
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2well, now you have a math problem. I suggest to ask this in math.SE. – Minimus Heximus Aug 03 '13 at 19:31
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You can look at an implementation of Bessel functions in any open source math library such as glibc. Porting one to the complex case would (hopefully!) consist of replacing `double` with `std::complex
` and compiling with a C++ compiler. Use your understanding of maths to refine the process. If you need this for work, consult your legal department first. – n. m. could be an AI Aug 03 '13 at 19:39 -
In that wiki page I see a series you can also approximate the value of the series in a function. Also see if the `
` header file has this fuctions predefined. – Minimus Heximus Aug 03 '13 at 19:39
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I haven't found that Boost is compatible with complex arguments (though it may a mistake on my part).
The FORTRAN code developed by D.E. Amos (the code used by MATLAB and others) is in the public domain and can be used by anybody. I have been developing a C++ interface to the library, extending it to the case of negative orders. You can check it out on GitHub.
Joey Dumont
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The Boost library implements ordinary Bessel functions of the first and second kind and modified Bessel functions of the first and second kind for both real and complex numbers (see documentation about Bessel functions).
Don't try to reinvent the wheel, just use the Boost implementation which is far superior to anything you could write yourself.
Kyle_the_hacker
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2This doesn't seem to be the case. I haven't been able to compile something like `std::cout << boost::math::cyl_bessel_j
> (0.0,std::complex – Joey Dumont Nov 04 '14 at 03:39(1.0,0.0)) << std::endl;` with Boost. -
Indeed, they don't seem to support complex arguments, if [this discussion](http://boost.2283326.n4.nabble.com/no-subject-td4478639.html) still represents current state. – Ruslan Jun 04 '15 at 12:58