antispam@math.uni.wroc.pl schrieb:   
   >   
   > clicliclic@freenet.de wrote:   
   > >   
   > > clicliclic@freenet.de schrieb:   
   > > >   
   > > > I should mention that my statements about Goursat integrability   
   > > > referred to Moebius mappings realizing the dihedral group D_2   
   > > > (isomorphic to the Klein four-group K_4) only; the special nature   
   > > > of the radicand x^3 - x may open other possibilities (thus, x <->   
   > > > 1/x swaps two roots and preserves the remaining two). Compare   
   > > > Goursat pp. 113-118 for x^3 - 1.   
   > > >   
   > >   
   > > Actually, Goursat considered the special radicand x^3 - x as well   
   > > (on pp. 118-119) and concludes that no special pseudo-elliptic cases   
   > > arise. I tend to believe him.   
   >   
   > Hmm, you checked that for order 3 one gets special case, Goursat   
   > says that there are none and you believe Goursat?  I do not   
   > understand.   
   >   
      
   Goursat claims ("... ne fournissent pas d'intégrales pseudo-elliptiques   
   nouvelles") that for the special radicand x^3 - x his method of Moebius   
   mapping cannot detect pseudo-elliptic integrands beyond those already   
   found from equation (5) on p. 111 of his paper.   
      
   For x^3 - 1, however, the situation is different (pp. 113-118).   
      
   Martin.   
      
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