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Gauss summation formula

  1. Oct 10, 2011 #1
    Why is the Gauss summation formula for complex parameters a,b,c: [tex]\displaystyle _2 F_1 (a,b;c;1) = \frac{\Gamma (c) \Gamma (c-a-b)}{\Gamma (c-a) \Gamma (c-b)}[/tex] only valid for [itex]\text{Re}(c-a-b)>0,\;c\neq 0,-1,-2,-3,...[/itex]?
  2. jcsd
  3. Oct 10, 2011 #2
    It makes sense that [itex]c\neq 0,-1,-2,-3,...[/itex] so that [itex]\Gamma (c)[/itex] is defined but why does [itex]\text{Re}(c-a-b)[/itex] have to be positive?
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