#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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Changes (by {'newvalue': u'Ralf Stephan', 'oldvalue': ''}):
* cc: chapoton (added)
* commit: => 191ca289d3c26813e0244251a983a62f2057347a
* status: new => needs_review
* author: => Ralf Stephan
Old description:
> At the moment everything Bessel is sent to mpmath and returns floating
> point but I,,n,,(0) and J,,n,,(0) are in (0,1). Also all I/J/K/Y,,n,,(x)
> with n in (-1/2,1/2) is a simple expression.
>
> For the latter see p.10 of
> http://www.math.psu.edu/papikian/Kreh.pdf
New description:
At the moment everything Bessel is sent to mpmath and returns floating
point but I,,n,,(0) and J,,n,,(0) are in (0,1). Also all I/J/K/Y,,n,,(x)
with n in (-1/2,1/2) is a simple expression.
For the latter see p.10 of
http://www.math.psu.edu/papikian/Kreh.pdf
This allows exact computation of series:
{{{
sage: bessel_I(2,x).series(x,10)
1/8*x^2 + 1/96*x^4 + 1/3072*x^6 + 1/184320*x^8 + Order(x^10)
}}}
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Comment:
New commits:
||[http://git.sagemath.org/sage.git/commit/?id=191ca289d3c26813e0244251a983a62f2057347a
191ca28]||{{{17678: special values of Bessel functions}}}||
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Ticket URL: <http://trac.sagemath.org/ticket/17678#comment:2>
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