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math/doc/issues.qbk
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2006-05-21 15:45:37 +00:00

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[section Known Issues, and Todo List]
[h4 tgamma]
* Can the __lanczos be optimized any further? (low priority)
[h4 lgamma]
* Improve accuracy near 1 and 2 with either Chebyshev or rational
approximation. (High priority).
[h4 erf/erfc]
* Rewrite using either Chebyshev or rational
approximation. (High priority).
[h4 Incomplete gamma]
* Implement Temme's asymptotic expansion for large a and z,
this one is mainly an issue of performance rather than accuracy (medium priority).
* Double check behavior of the upper fraction when a is very small and z -> 1 (Medium Priority).
* Double check behavior of the upper fraction when a is very small and z -> 0 (Medium Priority).
* Double check for opportunities to chain series expansions together, passing
the result of one into the initial value of the next (Medium Priority).
* Investigate asymptotic expansions for large a small z and large z small a
(see A&S) (low priority).
[h4 Beta Function]
* No known issues?
[h4 Incomplete Beta]
* Investigate Didonato and Morris' asymptotic expansion for large a and b
(medium priority).
* Double check for opportunities to chain series expansions together, passing
the result of one into the initial value of the next (Medium Priority).
* Investigate Didonato and Morris' asymptotic expansion for small a and b
(low priority).
[endsect]