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 | | http://functions.wolfram.com/07.23.03.b8nt.01 | 
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 | | Hypergeometric2F1[-(41/8), -(37/8), -(1/4), z] == 
 (-2 (-40641 + 3860895 z + 40730254 z^2 + 70844454 z^3 + 27588435 z^4 + 
     1851163 z^5) + (1/Sqrt[1 - z]) (81282 - 7762431 z - 65456707 z^2 - 
     33156646 z^3 + 76869980 z^4 + 28629429 z^5 + 795093 z^6))/
  (81282 2^(1/4) (1 + Sqrt[1 - z])^(3/4)) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["41", "8"]]], ",", RowBox[List["-", FractionBox["37", "8"]]], ",", RowBox[List["-", FractionBox["1", "4"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "40641"]], "+", RowBox[List["3860895", " ", "z"]], "+", RowBox[List["40730254", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["70844454", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["27588435", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1851163", " ", SuperscriptBox["z", "5"]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SqrtBox[RowBox[List["1", "-", "z"]]]], RowBox[List["(", RowBox[List["81282", "-", RowBox[List["7762431", " ", "z"]], "-", RowBox[List["65456707", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["33156646", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["76869980", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["28629429", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["795093", " ", SuperscriptBox["z", "6"]]]]], ")"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List["81282", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["3", "/", "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>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 41 </mn>  <mn> 8 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 37 </mn>  <mn> 8 </mn>  </mfrac>  </mrow>  </mrow>  <mo> ; </mo>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 1 </mn>  <mn> 4 </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[RowBox[List["-", FractionBox["41", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["37", "8"]]], 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["1", "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>  <mrow>  <mfrac>  <mn> 1 </mn>  <mrow>  <mn> 81282 </mn>  <mo> ⁢ </mo>  <mroot>  <mn> 2 </mn>  <mn> 4 </mn>  </mroot>  <mo> ⁢ </mo>  <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> 3 </mn>  <mo> / </mo>  <mn> 4 </mn>  </mrow>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mfrac>  <mrow>  <mrow>  <mn> 795093 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 28629429 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 76869980 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 33156646 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 65456707 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 7762431 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 81282 </mn>  </mrow>  <msqrt>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  </msqrt>  </mfrac>  <mo> - </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 1851163 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 27588435 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 70844454 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 40730254 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 3860895 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 40641 </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'> 41 <sep /> 8 </cn>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 37 <sep /> 8 </cn>  </apply>  </list>  <list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 1 <sep /> 4 </cn>  </apply>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 81282 </cn>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='rational'> 1 <sep /> 4 </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='rational'> 3 <sep /> 4 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 795093 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 28629429 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 76869980 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 33156646 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 65456707 </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'> 7762431 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='integer'> 81282 </cn>  </apply>  <apply>  <power />  <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>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 1851163 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 27588435 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 70844454 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 40730254 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 3860895 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> -40641 </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["41", "8"]]], ",", RowBox[List["-", FractionBox["37", "8"]]], ",", RowBox[List["-", FractionBox["1", "4"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "40641"]], "+", RowBox[List["3860895", " ", "z"]], "+", RowBox[List["40730254", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["70844454", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["27588435", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1851163", " ", SuperscriptBox["z", "5"]]]]], ")"]]]], "+", FractionBox[RowBox[List["81282", "-", RowBox[List["7762431", " ", "z"]], "-", RowBox[List["65456707", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["33156646", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["76869980", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["28629429", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["795093", " ", SuperscriptBox["z", "6"]]]]], SqrtBox[RowBox[List["1", "-", "z"]]]]]], RowBox[List["81282", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["3", "/", "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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