*To*: mathgroup@smc.vnet.net*Subject*: [mg11934] numerical evaluation of hypergeometric*From*: miglbaur@itp.tu-graz.ac.at (Hans Miglbauer)*Date*: Thu, 9 Apr 1998 00:33:39 -0400*Organization*: TU Graz

Hi, I have the following problem: The power series of the generalized hypergeometric function for its argument equal to unity, i.e., HypergeometricPFQ[ {a_1,..,a_p}, {b_1,..,b_q}, 1 ] converges absolutely, though very slowly, for apropriate real-parts of the parameters a_i, b_j. If the parameters are fixed, the function N[ ..., >>acc<< ] when applied to this hyp.geo. function seems to provide the numerical value with accuracy >>acc<<. Unfortunately, in some cases and for algebraic reasons the result seems to be far less accurate (or even wrong). Now I would like to ask You, what numerical algorithm is used by Mathematica for this task. Thanks! Hans Miglbauer