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 | | http://functions.wolfram.com/07.23.03.c4l0.01 | 
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 | | Hypergeometric2F1[13/8, 33/8, 21/4, z] == 
 (16 2^(1/4) (-312 (-1 + Sqrt[1 - z]) + 12 (-14 + Sqrt[1 - z]) z + 
    (-37 + 4 Sqrt[1 - z]) z^2 - 16 z^3))/(175 (1 + Sqrt[1 - z])^(1/4) 
   Sqrt[1 - z] z^4) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["13", "8"], ",", FractionBox["33", "8"], ",", FractionBox["21", "4"], ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List["16", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "312"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]]]], "+", RowBox[List["12", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "14"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "37"]], "+", RowBox[List["4", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], ")"]], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["16", " ", SuperscriptBox["z", "3"]]]]], ")"]]]], RowBox[List["175", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SuperscriptBox["z", "4"]]]]]]]] | 
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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>  <mi> F </mi>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mfrac>  <mn> 13 </mn>  <mn> 8 </mn>  </mfrac>  <mo> , </mo>  <mfrac>  <mn> 33 </mn>  <mn> 8 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mfrac>  <mn> 21 </mn>  <mn> 4 </mn>  </mfrac>  <mo> ; </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["13", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["33", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["21", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] </annotation>  </semantics>  <mo>  </mo>  <mfrac>  <mrow>  <mn> 16 </mn>  <mo> ⁢ </mo>  <mroot>  <mn> 2 </mn>  <mn> 4 </mn>  </mroot>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mn> 16 </mn>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <msqrt>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  </msqrt>  </mrow>  <mo> - </mo>  <mn> 37 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 12 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <msqrt>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  </msqrt>  <mo> - </mo>  <mn> 14 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mrow>  <mn> 312 </mn>  <mo> ⁢ </mo>  <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>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mn> 175 </mn>  <mo> ⁢ </mo>  <mroot>  <mrow>  <msqrt>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  </msqrt>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mn> 4 </mn>  </mroot>  <mo> ⁢ </mo>  <msqrt>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  </msqrt>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  </mfrac>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <cn type='rational'> 13 <sep /> 8 </cn>  <cn type='rational'> 33 <sep /> 8 </cn>  </list>  <list>  <cn type='rational'> 21 <sep /> 4 </cn>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> 16 </cn>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='rational'> 1 <sep /> 4 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -16 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 4 </cn>  <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>  </apply>  <cn type='integer'> -37 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 12 </cn>  <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'> -14 </cn>  </apply>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 312 </cn>  <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>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 175 </cn>  <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='rational'> 1 <sep /> 4 </cn>  </apply>  <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>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </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["Hypergeometric2F1", "[", RowBox[List[FractionBox["13", "8"], ",", FractionBox["33", "8"], ",", FractionBox["21", "4"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["16", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "312"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]]]], "+", RowBox[List["12", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "14"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "37"]], "+", RowBox[List["4", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], ")"]], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["16", " ", SuperscriptBox["z", "3"]]]]], ")"]]]], RowBox[List["175", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SuperscriptBox["z", "4"]]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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 | | HypergeometricPFQ[{},{},z] |  | HypergeometricPFQ[{},{b},z] |  | HypergeometricPFQ[{a},{},z] |  | HypergeometricPFQ[{a},{b},z] |  | HypergeometricPFQ[{a1},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] |  | HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] |  | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] |  | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] |  | HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] |  |  | 
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