> On January 26, 2006 3:32 PM Yigal Weinstein wrote: > > > > Is there a way in Axiom >= 3.9 to get a numerical approximation > > for Gamma(x,y)- without the use of NAG? I know there is for > > Gamma(x) but for incomplete gamma there seems no straightforward > > way. > On January 26, 2006 5:09 PM Vanuxem Grégory wrote: > > No :-( >
I suggest that someone tackle this problem based on the following article: http://www.theorie.physik.uni-muenchen.de/~serge/papers/Winitzki_2003_Comput ing_the_incomplete_Gamma_function_to_arbitrary_precision_LNCS_2667.pdf Computing the incomplete Gamma function to arbitrary precision Serge Winitzki1 Department of Physics, Ludwig-Maximilians University, Theresienstr. 37, 80333 Munich, Germany ([EMAIL PROTECTED]) Abstract. I consider an arbitrary-precision computation of the incomplete Gamma function from the Legendre continued fraction. Using the method of generating functions, I compute the convergence rate of the continued fraction and find a direct estimate of the necessary number of terms. This allows to compare the performance of the continued fraction and of the power series methods. As an application, I show that the incomplete Gamma function Gamma(a, z) can be computed to P digits in at most O (P) long multiplications uniformly in z for Re z > 0. The error function of the real argument, erf x, requires at most O(P2/3) long multiplications. -------- I would be glad to help someone with the SPAD coding. Regards, Bill Page. _______________________________________________ Axiom-math mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-math
