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numerical evaluation of hypergeometric

• 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