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 | | http://functions.wolfram.com/07.23.03.a9lb.01 | 
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 | | Hypergeometric2F1[-(19/4), 11/4, 1/2, z] == 
 (1/442) ((-(1 + Sqrt[z])^(5/2)) (-221 + 2120 Sqrt[z] + 888 z - 
     20560 z^(3/2) + 22000 z^2 + 23232 z^(5/2) - 45760 z^3 + 18304 z^(7/2)) + 
   (1 - Sqrt[z])^(5/2) (221 + 2120 Sqrt[z] - 888 z - 20560 z^(3/2) - 
     22000 z^2 + 23232 z^(5/2) + 45760 z^3 + 18304 z^(7/2))) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["19", "4"]]], ",", FractionBox["11", "4"], ",", FractionBox["1", "2"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "442"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], RowBox[List["5", "/", "2"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "221"]], "+", RowBox[List["2120", " ", SqrtBox["z"]]], "+", RowBox[List["888", " ", "z"]], "-", RowBox[List["20560", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["22000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["23232", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["45760", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["18304", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]], RowBox[List["5", "/", "2"]]], " ", RowBox[List["(", RowBox[List["221", "+", RowBox[List["2120", " ", SqrtBox["z"]]], "-", RowBox[List["888", " ", "z"]], "-", RowBox[List["20560", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["22000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["23232", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["45760", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["18304", " ", 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>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 19 </mn>  <mn> 4 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mfrac>  <mn> 11 </mn>  <mn> 4 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mfrac>  <mn> 1 </mn>  <mn> 2 </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[RowBox[List["-", FractionBox["19", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["1", "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> 442 </mn>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 5 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 18304 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 7 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 45760 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 23232 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 5 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 22000 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 20560 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 3 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 888 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mrow>  <mn> 2120 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  <mo> + </mo>  <mn> 221 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 5 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 18304 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 7 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 45760 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 23232 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 5 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 22000 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 20560 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 3 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 888 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mrow>  <mn> 2120 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  <mo> - </mo>  <mn> 221 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 19 <sep /> 4 </cn>  </apply>  <cn type='rational'> 11 <sep /> 4 </cn>  </list>  <list>  <cn type='rational'> 1 <sep /> 2 </cn>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='rational'> 1 <sep /> 442 </cn>  <apply>  <plus />  <apply>  <times />  <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'> 5 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 18304 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 7 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 45760 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 23232 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 5 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 22000 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 20560 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 3 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 888 </cn>  <ci> z </ci>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 2120 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> 221 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <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'> 5 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 18304 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 7 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 45760 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 23232 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 5 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 22000 </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'> 20560 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 3 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 888 </cn>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> 2120 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -221 </cn>  </apply>  </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[RowBox[List["-", FractionBox["19", "4"]]], ",", FractionBox["11", "4"], ",", FractionBox["1", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "442"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], RowBox[List["5", "/", "2"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "221"]], "+", RowBox[List["2120", " ", SqrtBox["z"]]], "+", RowBox[List["888", " ", "z"]], "-", RowBox[List["20560", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["22000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["23232", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["45760", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["18304", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]], RowBox[List["5", "/", "2"]]], " ", RowBox[List["(", RowBox[List["221", "+", RowBox[List["2120", " ", SqrtBox["z"]]], "-", RowBox[List["888", " ", "z"]], "-", RowBox[List["20560", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["22000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["23232", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["45760", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["18304", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]]]]]], ")"]]]]]]]] | 
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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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