Hi all, I hope this is not considered too off-topic: my question refers to a third-party extension to GSL (for Jacobi polynomials), but I am hoping the mathematical experts here may be able to point me in the right direction.
I have been using the contributed extension found here: http://www.network-theory.co.uk/download/gslextras/Jacobi/ This works ok up to a point, but the recurrence relation suffers from catastrophic cancelation under some circumstances, such as x->1 for large n and negative a. I attempted to enhance the code by implementing an alternative method based on series summation. The original reference for this method is as follows (though I have not yet been able to acquire this primary reference): G. Szego, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ., Vol. 23, Amer. Math. Soc., p62 Unfortunately, there are some circumstances when BOTH methods suffer from cancelation e.g. P_34^(-16,16) for x~0.8055. I am therefore rather stuck as to how I can obtain an accurate answer for cases such as this. I notice that Mathematica is able to give an accurate answer in such cases, but I have no idea how to go about calculating that answer myself (I am mathematically out of my depth with this sort of thing). Should I be looking for yet another way of generating the Jacobi function, or do I simply need to resort to higher precision arithmetic in these pathological cases? Thanks in advance for any suggestions! Jonny _______________________________________________ Help-gsl mailing list [email protected] http://lists.gnu.org/mailman/listinfo/help-gsl
