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   http://functions.wolfram.com/07.24.03.0050.01
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    Hypergeometric2F1Regularized[a, (1 - a)/3, (4 a + 5)/6, -(1/8)] == 
 (2^(-1 + a) Gamma[1/6 + a/3])/(Sqrt[Pi] Gamma[1/2 + a]) 
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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>  <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>  <mi> a </mi>  <mo> , </mo>  <mfrac>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> a </mi>  </mrow>  <mn> 3 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mfrac>  <mrow>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <mi> a </mi>  </mrow>  <mo> + </mo>  <mn> 5 </mn>  </mrow>  <mn> 6 </mn>  </mfrac>  <mo> ; </mo>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 1 </mn>  <mn> 8 </mn>  </mfrac>  </mrow>  </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["a", Hypergeometric2F1Regularized, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["1", "-", "a"]], "3"], Hypergeometric2F1Regularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List[RowBox[List["4", "a"]], "+", "5"]], "6"], Hypergeometric2F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["1", "8"]]], Hypergeometric2F1Regularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1Regularized] </annotation>  </semantics>  <mo> ⩵ </mo>  <mfrac>  <mrow>  <msup>  <mn> 2 </mn>  <mrow>  <mi> a </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mfrac>  <mi> a </mi>  <mn> 3 </mn>  </mfrac>  <mo> + </mo>  <mfrac>  <mn> 1 </mn>  <mn> 6 </mn>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <msqrt>  <mi> π </mi>  </msqrt>  <mo> ⁢ </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mfrac>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> Hypergeometric2F1Regularized </ci>  <ci> a </ci>  <apply>  <times />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> a </ci>  </apply>  </apply>  <apply>  <power />  <cn type='integer'> 3 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 4 </cn>  <ci> a </ci>  </apply>  <cn type='integer'> 5 </cn>  </apply>  <apply>  <power />  <cn type='integer'> 6 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 1 <sep /> 8 </cn>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <cn type='integer'> 2 </cn>  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <ci> Gamma </ci>  <apply>  <plus />  <apply>  <times />  <ci> a </ci>  <apply>  <power />  <cn type='integer'> 3 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <cn type='rational'> 1 <sep /> 6 </cn>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <apply>  <power />  <pi />  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <ci> Gamma </ci>  <apply>  <plus />  <ci> a </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   
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  | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["a_", ",", FractionBox[RowBox[List["1", "-", "a_"]], "3"], ",", RowBox[List[FractionBox["1", "6"], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", "a_"]], "+", "5"]], ")"]]]], ",", RowBox[List["-", FractionBox["1", "8"]]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "+", "a"]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "6"], "+", FractionBox["a", "3"]]], "]"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "a"]], "]"]]]]]]]]]  |  
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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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