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 | | http://functions.wolfram.com/07.23.03.bamy.01 | 
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 | | Hypergeometric2F1[-(39/8), 37/8, 5/4, z] == 
 (1/(505325 z)) (2^(1/4) (1 + Sqrt[1 - z])^(3/4) 
   (121923 - 3541519 z + 21512352 z^2 - 49277184 z^3 + 47902720 z^4 - 
    16711680 z^5 + (1/Sqrt[1 - z]) (-121923 + 3855143 z - 27904228 z^2 + 
      83064320 z^3 - 119514112 z^4 + 82903040 z^5 - 22282240 z^6))) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["39", "8"]]], ",", FractionBox["37", "8"], ",", FractionBox["5", "4"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["505325", " ", "z"]]], RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List["121923", "-", RowBox[List["3541519", " ", "z"]], "+", RowBox[List["21512352", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["49277184", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["47902720", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["16711680", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List[FractionBox["1", SqrtBox[RowBox[List["1", "-", "z"]]]], RowBox[List["(", RowBox[List[RowBox[List["-", "121923"]], "+", RowBox[List["3855143", " ", "z"]], "-", RowBox[List["27904228", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["83064320", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["119514112", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["82903040", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["22282240", " ", SuperscriptBox["z", "6"]]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]] | 
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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> 39 </mn>  <mn> 8 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mfrac>  <mn> 37 </mn>  <mn> 8 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mfrac>  <mn> 5 </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[RowBox[List["-", FractionBox["39", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[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[FractionBox["5", "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> 505325 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <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>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mn> 16711680 </mn>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 47902720 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 49277184 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 21512352 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 3541519 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <msqrt>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  </msqrt>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mn> 22282240 </mn>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 82903040 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 119514112 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 83064320 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 27904228 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 3855143 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 121923 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 121923 </mn>  </mrow>  <mo> ) </mo>  </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'> 39 <sep /> 8 </cn>  </apply>  <cn type='rational'> 37 <sep /> 8 </cn>  </list>  <list>  <cn type='rational'> 5 <sep /> 4 </cn>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 505325 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <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>  <plus />  <apply>  <times />  <cn type='integer'> -16711680 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 47902720 </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'> 49277184 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 21512352 </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'> 3541519 </cn>  <ci> z </ci>  </apply>  </apply>  <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>  <ci> z </ci>  </apply>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -22282240 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 82903040 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 119514112 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 83064320 </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'> 27904228 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 3855143 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> -121923 </cn>  </apply>  </apply>  <cn type='integer'> 121923 </cn>  </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["39", "8"]]], ",", FractionBox["37", "8"], ",", FractionBox["5", "4"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List["121923", "-", RowBox[List["3541519", " ", "z"]], "+", RowBox[List["21512352", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["49277184", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["47902720", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["16711680", " ", SuperscriptBox["z", "5"]]], "+", FractionBox[RowBox[List[RowBox[List["-", "121923"]], "+", RowBox[List["3855143", " ", "z"]], "-", RowBox[List["27904228", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["83064320", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["119514112", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["82903040", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["22282240", " ", SuperscriptBox["z", "6"]]]]], SqrtBox[RowBox[List["1", "-", "z"]]]]]], ")"]]]], RowBox[List["505325", " ", "z"]]]]]]] | 
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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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