In addition to John's detailed responses... I've got a few ideas for Boost.Math that might be acceptable for the scope of your project. I would be interested in looking into new functions such as those related to the Lerch transcendental (Zeta, Hurwitz Zeta, Polygamma for wider argument range, etc.).
To add to those are the hypergeometric functions 1F1 and 2F1, note however that these are not only hard to implement well, but they are practically untestable (too many arguments). Unfortunately they are also very useful! A good research project though...
Oh, the list goes on and on...
Yudell Luke's classic books have some algorithms on multi-term
recurrence relations of generalized hypergeometric functions pFq
in some parameter regions. I have extended some of these to float,
double, long double, multiprecision, for real and complex for certain
parameter regions.
I can confirm that computing hypergeometric functions over wide
ranges of parameters is difficult, and couldpotentially comprise
a rich research topic.
I can provide some starting points for calculating some of
these functions, if requested.
Sincerely, Chris.
On Friday, November 1, 2013 1:12 PM, John Maddock
In addition to John's detailed responses... I've got a few ideas for Boost.Math that might be acceptable for the scope of your project. I would be interested in looking into new functions such as those related to the Lerch transcendental (Zeta, Hurwitz Zeta, Polygamma for wider argument range, etc.).
To add to those are the hypergeometric functions 1F1 and 2F1, note however that these are not only hard to implement well, but they are practically untestable (too many arguments). Unfortunately they are also very useful! A good research project though... John. _______________________________________________ Unsubscribe & other changes: http://lists.boost.org/mailman/listinfo.cgi/boost