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 | | http://functions.wolfram.com/07.23.03.amht.01 | 
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 | | Hypergeometric2F1[13/4, 23/4, -(9/2), z] == 
 (1/20160) ((1/(1 - Sqrt[z])^(27/2)) (10080 - 136080 Sqrt[z] + 808640 z - 
     2695140 z^(3/2) + 5197770 z^2 - 5037345 z^(5/2) + 1039554 z^3 - 
     77004 z^(7/2)) + (1/(1 + Sqrt[z])^(27/2)) (10080 + 136080 Sqrt[z] + 
     808640 z + 2695140 z^(3/2) + 5197770 z^2 + 5037345 z^(5/2) + 
     1039554 z^3 + 77004 z^(7/2))) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["13", "4"], ",", FractionBox["23", "4"], ",", RowBox[List["-", FractionBox["9", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "20160"], RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]], RowBox[List["27", "/", "2"]]]], RowBox[List["(", RowBox[List["10080", "-", RowBox[List["136080", " ", SqrtBox["z"]]], "+", RowBox[List["808640", " ", "z"]], "-", RowBox[List["2695140", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["5197770", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["5037345", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["1039554", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["77004", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], RowBox[List["27", "/", "2"]]]], RowBox[List["(", RowBox[List["10080", "+", RowBox[List["136080", " ", SqrtBox["z"]]], "+", RowBox[List["808640", " ", "z"]], "+", RowBox[List["2695140", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["5197770", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5037345", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["1039554", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["77004", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]]]]]], ")"]]]]]]]] | 
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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> 4 </mn>  </mfrac>  <mo> , </mo>  <mfrac>  <mn> 23 </mn>  <mn> 4 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 9 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <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", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["23", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["9", "2"]]], 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>  <mrow>  <mfrac>  <mn> 1 </mn>  <mn> 20160 </mn>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mfrac>  <mn> 1 </mn>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 27 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mn> 77004 </mn>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 7 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 1039554 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 5037345 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 5 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 5197770 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 2695140 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 3 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 808640 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mrow>  <mn> 136080 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  <mo> + </mo>  <mn> 10080 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 27 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 77004 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 7 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 1039554 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 5037345 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 5 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 5197770 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 2695140 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 3 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 808640 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mrow>  <mn> 136080 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  <mo> + </mo>  <mn> 10080 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <cn type='rational'> 13 <sep /> 4 </cn>  <cn type='rational'> 23 <sep /> 4 </cn>  </list>  <list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 9 <sep /> 2 </cn>  </apply>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='rational'> 1 <sep /> 20160 </cn>  <apply>  <plus />  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <cn type='rational'> 27 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -77004 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 7 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 1039554 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 5037345 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 5 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 5197770 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 2695140 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 3 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 808640 </cn>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 136080 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <cn type='integer'> 10080 </cn>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <power />  <apply>  <plus />  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <cn type='rational'> 27 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 77004 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 7 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 1039554 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 5037345 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 5 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 5197770 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 2695140 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 3 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 808640 </cn>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> 136080 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> 10080 </cn>  </apply>  </apply>  </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", "4"], ",", FractionBox["23", "4"], ",", RowBox[List["-", FractionBox["9", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[FractionBox[RowBox[List["10080", "-", RowBox[List["136080", " ", SqrtBox["z"]]], "+", RowBox[List["808640", " ", "z"]], "-", RowBox[List["2695140", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["5197770", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["5037345", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["1039554", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["77004", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]], RowBox[List["27", "/", "2"]]]], "+", FractionBox[RowBox[List["10080", "+", RowBox[List["136080", " ", SqrtBox["z"]]], "+", RowBox[List["808640", " ", "z"]], "+", RowBox[List["2695140", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["5197770", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5037345", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["1039554", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["77004", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], RowBox[List["27", "/", "2"]]]]]], "20160"]]]]] | 
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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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