#3426: [with new patch, needs review] bessel_K function is broken
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Reporter: bober | Owner: gfurnish
Type: defect | Status: new
Priority: major | Milestone: sage-3.2
Component: calculus | Resolution:
Keywords: bessel, bessel_K, editor_gfurnish |
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Changes (by AlexGhitza):
* cc: AlexGhitza (removed)
* summary: [with patch, needs work] bessel_K function is broken => [with
new patch, needs review] bessel_K function is
broken
Comment:
I looked up the definition and properties of the Bessel functions in
several references (Section 7.2 of the "Bateman Manuscript Project",
for instance).
I uploaded a brand new patch that implements the behavior described
there, namely returning a real number if the result is theoretically
known to be real, and a complex number otherwise. I added doctests
that document this behavior, and checked all of them against
Mathematica. I did this for all three Bessel functions that are
implemented in special.py using Pari, namely J, K, and I. I also put in a
workaround for a silly Pari buglet that
complains about negative integer values of nu.
In the process I uncovered a couple of unrelated issues with
special.py and Bessel functions, for which I'll open separate tickets.
The patch is made against 3.1.3.alpha2.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3426#comment:27>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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