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   http://functions.wolfram.com/07.24.04.0003.02
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    Hypergeometric2F1Regularized[Conjugate[a], Conjugate[b], Conjugate[c], 
   Conjugate[z]] == Conjugate[Hypergeometric2F1Regularized[a, b, c, z]] /; 
  !IntervalMemberQ[Interval[{1, Infinity}], z] 
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   <math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'>  <semantics>  <mrow>  <mrow>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 2 </mn>  </msub>  <msub>  <mover>  <mi> F </mi>  <mo> ~ </mo>  </mover>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <semantics>  <mrow>  <mover>  <mi> a </mi>  <mo> _ </mo>  </mover>  <mo> , </mo>  <mover>  <mi> b </mi>  <mo> _ </mo>  </mover>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[TagBox[OverscriptBox["a", "_"], Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[OverscriptBox["b", "_"], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]] </annotation>  </semantics>  <mo> ; </mo>  <semantics>  <mover>  <mi> c </mi>  <mo> _ </mo>  </mover>  <annotation encoding='Mathematica'> TagBox[TagBox[TagBox[OverscriptBox["c", "_"], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]] </annotation>  </semantics>  <mo> ; 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  | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List[RowBox[List["Conjugate", "[", "a_", "]"]], ",", RowBox[List["Conjugate", "[", "b_", "]"]], ",", RowBox[List["Conjugate", "[", "c_", "]"]], ",", RowBox[List["Conjugate", "[", "z_", "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Conjugate", "[", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["a", ",", "b", ",", "c", ",", "z"]], "]"]], "]"]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["1", ",", "\[Infinity]"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]  |  
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   Date Added to functions.wolfram.com (modification date)
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| HypergeometricPFQRegularized[{},{b},z] |  | HypergeometricPFQRegularized[{a1},{b1},z] |  | HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] |  |   |  
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