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   http://functions.wolfram.com/07.24.26.0043.01
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    (1 + Sqrt[1 - z])^(1 - b - c) Hypergeometric2F1Regularized[1, b, c, 
   (-1 + Sqrt[1 - z])/(1 + Sqrt[1 - z])] == (1/(2 Sqrt[Pi] Gamma[c - 1])) 
  MeijerG[{{1 - (b + c)/2, (3 - b - c)/2, 2 - c}, {}}, 
   {{0}, {2 - b - c, 1 - c}}, -z] 
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   Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "-", "b", "-", "c"]]], " ", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["1", ",", "b", ",", "c", ",", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", SqrtBox["\[Pi]"], RowBox[List["Gamma", "[", RowBox[List["c", "-", "1"]], "]"]]]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox[RowBox[List["b", "+", "c"]], "2"]]], ",", FractionBox[RowBox[List["3", "-", "b", "-", "c"]], "2"], ",", RowBox[List["2", "-", "c"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "-", "b", "-", "c"]], ",", RowBox[List["1", "-", "c"]]]], "}"]]]], "}"]], ",", RowBox[List["-", "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>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <msqrt>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  </msqrt>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> b </mi>  <mo> - </mo>  <mi> c </mi>  </mrow>  </msup>  <mo> ⁢ </mo>  <semantics>  <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>  <mrow>  <mn> 1 </mn>  <mo> , </mo>  <mi> b </mi>  </mrow>  <mo> ; </mo>  <mi> c </mi>  <mo> ; </mo>  <mfrac>  <mrow>  <msqrt>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  </msqrt>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mrow>  <msqrt>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  </msqrt>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", Hypergeometric2F1Regularized, Rule[Editable, True]], ",", TagBox["b", Hypergeometric2F1Regularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox["c", Hypergeometric2F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "-", "1"]], RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", "1"]]], Hypergeometric2F1Regularized, Rule[Editable, 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<mi> b </mi>  <mo> - </mo>  <mi> c </mi>  </mrow>  <mn> 2 </mn>  </mfrac>  <mo> , </mo>  <mrow>  <mn> 2 </mn>  <mo> - </mo>  <mi> c </mi>  </mrow>  </mrow>  </mtd>  </mtr>  <mtr>  <mtd>  <mrow>  <mn> 0 </mn>  <mo> , </mo>  <mrow>  <mn> 2 </mn>  <mo> - </mo>  <mi> b </mi>  <mo> - </mo>  <mi> c </mi>  </mrow>  <mo> , </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> c </mi>  </mrow>  </mrow>  </mtd>  </mtr>  </mtable>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["3", ",", "3"]], RowBox[List["1", ",", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List["-", "z"]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", FractionBox[RowBox[List["b", "+", "c"]], "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["3", "-", "b", "-", "c"]], "2"], MeijerG, Rule[Editable, True]], 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Hypergeometric2F1Regularized </ci>  <cn type='integer'> 1 </cn>  <ci> b </ci>  <ci> c </ci>  <apply>  <times />  <apply>  <plus />  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  <apply>  <power />  <apply>  <plus />  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <pi />  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <ci> Gamma </ci>  <apply>  <plus />  <ci> c </ci>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <ci> MeijerG </ci>  <list>  <list>  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <plus />  <ci> b </ci>  <ci> c </ci>  </apply>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <plus />  <cn type='integer'> 3 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> b </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  </apply>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <cn type='integer'> 2 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  </apply>  </list>  <list />  </list>  <list>  <list>  <cn type='integer'> 0 </cn>  </list>  <list>  <apply>  <plus />  <cn type='integer'> 2 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> b </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  </apply>  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  </apply>  </list>  </list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   
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  | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z_"]]]]], ")"]], RowBox[List["1", "-", "b_", "-", "c_"]]], " ", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["1", ",", "b_", ",", "c_", ",", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z_"]]]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z_"]]]]]]]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox[RowBox[List["b", "+", "c"]], "2"]]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["3", "-", "b", "-", "c"]], ")"]]]], ",", RowBox[List["2", "-", "c"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "-", "b", "-", "c"]], ",", RowBox[List["1", "-", "c"]]]], "}"]]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List["c", "-", "1"]], "]"]]]]]]]]]  |  
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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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