#17678: special values of Bessel functions
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Reporter: rws | Owner:
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-6.5
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: Ralf Stephan | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/rws/special_values_of_bessel_functions|
191ca289d3c26813e0244251a983a62f2057347a
Dependencies: | Stopgaps:
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Comment (by rws):
Replying to [comment:6 kcrisman]:
> Question: [http://www.wolframalpha.com/input/?i=besselj%28-5%2F2%2C0%29
W|A claims] that one has the complex infinity, not positive infinity, for
some of the negative ones like `bessel_J(-5/2, 0)` or for `bessel_I`. I
don't know what to make of that, though.
I got those values from mpmath and just tried to post about that to the
mpmath group, but not yet approved.
> Also, does `bessel_Y` have an analogous special value for x=0, negative
n?
Ah, I missed that. It should be easily derived from `Bessel_J` with
Y,,n,,(z)=(J,,n,,(z)*cos(n*pi)-J,,-n,,(z))/sin(n*pi) (Abramowitz and
Stegun 1972, p. 358).
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Ticket URL: <http://trac.sagemath.org/ticket/17678#comment:7>
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