Now toolbox has new engine for basic array manipulation operations, see http://goo.gl/mBJrk7
Basically it is up to 4 times faster (2 in average). Hopefully this be useful.

This function has been added to toolbox.

Toolbox is not meant to replace the double precision computations.

Extended precision provided in toolbox is targeted to solve problems, which are not solvable in double precision (sensitive eigenvalues, ill-conditioned systems, etc.).

What comparison is possible here ;)? Solved / Not solved?

Speed is irrelevant if problem is not solved, right?

That is because toolbox switches to multiprecision mode (if necessary) - to compute the bessel accurately.

Now toolbox is using adaptive algorithm for series summation - every operation is analysed for cancellation/rounding errors. 
If it is of unacceptable level - precision is boosted up to compensate the issue. At the end we re-arrange the terms to guarantee the minimum accuracy loss overall [1]. 

It will became much faster in future, when we will add asymptotics for large arguments and (probably) simplify the algorithm.

Hope it is useful for your work.

Btw, our system solver has been updated today with faster decompositions under the hood. You might see some changes in computing time.

[1]. J. Demmel. Y. Hida. Fast and accurate floating point summation with application to computational geometry.

Compilation for Windows just has been finished: http://goo.gl/jcoexM

Would appreciate your feedback.

Michael,

I have just released Linux version of toolbox with fixed bessely: http://goo.gl/btsBt
(you use Linux version, right?)

Now it provides accurate result up to the last digit of precision specified (and last digit is correctly rounded).
The main drawback - function is slow for large arguments. Will improve this in next updates.

Please test it in your conditions.

New GNU Linux version has been released (which includes fix for the issue among other improvements).

Please download it using the usual link: http://goo.gl/btsBt