Opened 13 years ago

Closed 8 years ago

# implement arbitrary precision Bessel Y function

Reported by: Owned by: AlexGhitza burcin minor sage-duplicate/invalid/wontfix calculus kcrisman, benjaminfjones Karl-Dieter Crisman, Benjamin Jones N/A

### 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.

### comment:1 Changed 13 years ago by ddrake

It would also be nice to be able to evaluate Bessel functions with complex, or at least purely imaginary, arguments.

### comment:2 Changed 13 years ago by AlexGhitza

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 ddrake

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 kcrisman

• Report Upstream set to N/A

### comment:5 Changed 8 years ago by kcrisman

This would most likely be fixed by #4102.

### comment:6 Changed 8 years ago by benjaminfjones

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 kcrisman

• 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.

Version 0, edited 8 years ago by kcrisman (next)

### comment:8 Changed 8 years ago by kcrisman

• Status changed from needs_review to positive_review

### comment:9 Changed 8 years ago by jdemeyer

• Resolution set to duplicate
• Status changed from positive_review to closed
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