I'm trying to figure out what library is the most accurate to date. I use in my codes GSL (GNU Scientific Library) which the most complete I found so far. Do you prefer something else, especially for special functions like Bessel and Neumann? Those are the ones I'm most interested in.
I am mostly using libraries for linear algebra, e.g. Armadillo or Eigenlib. In general I like to use the Boost library for many different things. They also have Bessel functions. They tend to have a very high accuracy. Just have a look at their comparison to GSL:
http://www.boost.org/doc/libs/1_35_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html#math_toolkit.special.bessel.bessel.accuracy
I'm using boost and Intel's MKL. The MKL ofers usually great performance, on the other hand, it isn't free....
You can also take a look at the python packages scipy and numpy. You can still call these from C/C++ environments as well. I highly recommend the series of books written by Hans Peter Langtangen on computational python.
Some resources are:
http://www.johndcook.com/Bessel_python.html
https://github.com/GrahamDennis/xpdeint/blob/master/xpdeint/Features/Transforms/_BesselTransform.py
http://docs.scipy.org/doc/numpy/reference/generated/numpy.i0.html
http://www.amazon.com/Python-Scripting-Computational-Science-Engineering/dp/3540739157/ref=sr_1_2?ie=UTF8&qid=1395338893&sr=8-2&keywords=langtangen
http://www.scientificpython.net/1/category/all/1.html
This might ba a good moment to mention the XSC library:
http://www.xsc.de
Also, it should be noted that MKL is *not* the only BLAS implementation - there are some free and open ones - possibly worse than MKL (are they?), but certainly nice, e.g., OpenBLAS.
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