#16813: symbolic Legendre / associated Legendre functions / polynomials
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       Reporter:  rws          |        Owner:
           Type:  enhancement  |       Status:  new
       Priority:  major        |    Milestone:  sage-6.4
      Component:  symbolics    |   Resolution:
       Keywords:               |    Merged in:
        Authors:               |    Reviewers:
Report Upstream:  N/A          |  Work issues:
         Branch:               |       Commit:
   Dependencies:               |     Stopgaps:
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Comment (by rws):

 Some timings for P(n,z):
 {{{
 sage: legendre_P(100,2.5)
 6.39483750487443e66
 sage: timeit('legendre_P(100,2.5)')
 25 loops, best of 3: 21 ms per loop

 sage: from mpmath import legenp
 sage: legenp(100,0,2.5)
 mpf('6.3948375048744286e+66')
 sage: timeit('legenp(100,0,2.5)')
 625 loops, best of 3: 97.2 µs per loop

 sage: from scipy.special import eval_legendre
 sage: eval_legendre(int(100),float(2.5))
 6.3948375048744324e+66
 sage: timeit('eval_legendre(int(100),float(2.5))')
 625 loops, best of 3: 7.62 µs per loop

 sage: eval_legendre(int(10^5),float(1.00001))
 3.1548483029540554e+192
 sage: timeit('eval_legendre(int(10^6),float(2.5))')
 25 loops, best of 3: 11.8 ms per loop
 sage: eval_legendre(int(10^6),float(2.5))
 inf

 }}}
 while `legenp` will already bail out at 10^5^ because of F convergence
 issues.

--
Ticket URL: <http://trac.sagemath.org/ticket/16813#comment:6>
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