#15024: Add Hankel functions and make spherical Bessel and Hankel functions
symbolic
-------------------------------------+-------------------------------------
Reporter: eviatarbach | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: Eviatar Bach, | Reviewers:
Ralf Stephan | Work issues:
Report Upstream: N/A | Commit:
Branch: | e1b4ee098d002ddd794acde0833b2b3f31d0c888
u/rws/add_hankel_functions_and_make_spherical_bessel_and_hankel_functions_symbolic|
Stopgaps:
Dependencies: #18257 |
-------------------------------------+-------------------------------------
Changes (by kcrisman):
* status: needs_review => needs_work
Comment:
[http://en.wikipedia.org/wiki/Bessel_function#Spherical_Bessel_functions:_jn.2C_yn
Wikipedia] and [http://dlmf.nist.gov/10.51 DLMF] agree that the derivative
formulas for the various spherical functions only apply if the index is an
integer. I'm not sure how this connects to
[http://www.wolframalpha.com/input/?i=derivative+of+spherical+bessel+j
W|A]'s solution to that.
Also
{{{
sage: integrate(spherical_bessel_J(1,x)^2,(x,0,oo))
1/6*pi
sage: integrate(spherical_bessel_Y(1,x)^2,(x,0,oo))
-1/6*pi
}}}
is just too cool not to include.
This is very nicely put together and other than these comments mostly
needs just pseudo-random testing that mpmath or whoever doesn't have any
weird error spots. 'Needs work' for updating updating documentation,
otherwise 'needs info' for the other points raised.
--
Ticket URL: <http://trac.sagemath.org/ticket/15024#comment:21>
Sage <http://www.sagemath.org>
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