Opened 13 years ago
Closed 8 years ago
#4230 closed enhancement (duplicate)
implement arbitrary precision Bessel Y function
Reported by: | AlexGhitza | Owned by: | burcin |
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Priority: | minor | Milestone: | sage-duplicate/invalid/wontfix |
Component: | calculus | Keywords: | |
Cc: | kcrisman, benjaminfjones | Merged in: | |
Authors: | Reviewers: | Karl-Dieter Crisman, Benjamin Jones | |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
At the moment, Sage uses Maxima to compute the Bessel Y function. This is slow and works only with the default 53 bits of precision. It would be fairly easy to implement this:
- for integer values of the order nu, use the mpfr yn function
- for non-integer values of nu, use the formula $Y_nu(z) = (J_nu(z)*cos(nu*pi) - J_{-nu}(z))/sin(nu*pi)$, where J is the Bessel J function.
Change History (9)
comment:1 Changed 13 years ago by
comment:2 Changed 13 years ago by
See #3426 (and review it!) for the Bessel functions other than Y. The code computes values at arbitrary complex coefficients.
comment:3 Changed 12 years ago by
Now that mpmath is included in Sage, why not just use mpmath's Bessel functions? http://mpmath.googlecode.com/svn/trunk/doc/build/functions/bessel.html
They seem to be very well-implemented, work to arbitrary precision, take complex arguments, and so on. Is this a good idea?
comment:4 Changed 10 years ago by
- Cc kcrisman added
- Report Upstream set to N/A
comment:6 Changed 8 years ago by
Yep, I'll add a related doctest in #4102 to address arbitrary precision numerical evaluation for bessel_Y.
comment:7 Changed 8 years ago by
- Milestone changed from sage-5.7 to sage-duplicate/invalid/wontfix
- Reviewers set to Karl-Dieter Crisman, Benjamin Jones
- Status changed from new to needs_review
Confirmed that this is done there.
comment:8 Changed 8 years ago by
- Status changed from needs_review to positive_review
comment:9 Changed 8 years ago by
- Resolution set to duplicate
- Status changed from positive_review to closed
It would also be nice to be able to evaluate Bessel functions with complex, or at least purely imaginary, arguments.