Re: Hypergeometric function

*To*: mathgroup at smc.vnet.net*Subject*: [mg50209] Re: Hypergeometric function*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Fri, 20 Aug 2004 04:58:06 -0400 (EDT)*Organization*: The University of Western Australia*References*: <cg20ms$p0q$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <cg20ms$p0q$1 at smc.vnet.net>, jujio77 at yahoo.com (Scott) wrote: > I have a finite alternating series of hypergeometric (2F1) functions. Why not give the series? > These functions have complex parameters. When I sum the series I get > larger and larger values. THen perhaps it is divergent? > My question is this, does anyone know how > precise Mathematica is when calculating a hypergeometric fn > numerically ie, how many sig figs are correct? Are you working with machine precision or arbitrary precision? For example, compare machine = Hypergeometric2F1[1 + 2 I, 2 - I, 3 - I, 0.95] with arbitrary = Hypergeometric2F1[1 + 2 I, 2 - I, 3 - I, 0.95`30] In the second case the argument is given with Precision 30. If you compute the difference between these expressions machine - arbitrary you will see that the machine precision result is correct to MachinePrecision. > I have done various transformations on the hypergeometric fn and then > summed the series. Each time I arrive at the same result. Which is good to hear, at least from a consistency viewpoint. Cheers, Paul -- Paul Abbott Phone: +61 8 9380 2734 School of Physics, M013 Fax: +61 8 9380 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul