AppellF1 Question

*To*: mathgroup at smc.vnet.net*Subject*: [mg48144] AppellF1 Question*From*: "Christos Argyropoulos MD" <chrisarg at medscape.com>*Date*: Fri, 14 May 2004 20:58:58 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hi everyone, I have been playing recently with the AppellF1 function as implemented in Mathematica 4.2 (Running under Wi(n)dowsXP) when I noticed the following: for certain combinations of arguments Mathematica returns the function un-evaluated (even after explicitly asking for a numerical result). Sure one can use any of the 5 general transformations to get an answer, but , it would be incovenient to have to check against these "pathological case". Here's an example (more can be found): In[1]:= AppellF1[2.`,-1.`,2.`,4.`,3.5`,-11.500000000000002`] Out[1]= AppellF1[2.,-1.,2.,4.,3.5,-11.5] The 1000000$ question is whether, such behaviour is to be expected (I naively expected that the implementation would yield an answer for all real arguments since no documentation to the contrary can be found in the online help or the Mathematica book). As a passing note, 3 out of the 5 general transformations of the AppellF1 function listed under Major General Identities (http://functions.wolfram.com/HypergeometricFunctions/AppellF1/17/01/0 1/) in the Wolfram Function web site seem to be (?incorrectly) restricted to cases where z1 < 1 & z2 < 1. The same transformations as appearing in the Bateman Manuscript (p239, 240 1955 McGrawHill Edition) are not restricted to particular values for z1, z2. Christos Argyropoulos MD PAtras Greece Sent by Medscape Mail: Free Portable E-mail for Professionals on the Move http://www.medscape.com