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MathGroup Archive 2004

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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

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