问题
How can I integrate an equation including bessel functions numerically from "0" to "infinity" in Fortran or/and C? I did in matlab, but it's not true for larger inputs and after a specific values , the bessel functions give completely wrong results(there is a restriction in Matlab)
回答1:
You can pretty much google and find lots of Bessel functions implemented in C already.
http://www.atnf.csiro.au/computing/software/gipsy/sub/bessel.c
http://jean-pierre.moreau.pagesperso-orange.fr/c_bessel.html
https://msdn.microsoft.com/en-us/library/h7zkk1bz.aspx
In the end, these use the built in types and will be limited to the ranges they can represent (just as MATLAB is). At best, expect 15 digits of precision using double precision floating point representation. So, for large numbers, they will appear to be rounded. eg. 1237846464123450000000000.00000
And, of course, others on Stack Overflow have looked into it.
C++ Bessel function for complex numbers
回答2:
There's a large number of analytic results for various integrals of the Bessel functions (see DLMF, Sect. 10.22), including definite integrals over precisely this range. You'd be much better off, and almost certainly faster and more accurate, trying hard to recast your expression into something that's integrable and using an exact result.
来源：https://stackoverflow.com/questions/29145922/integration-of-bessel-functions-in-c-fortran