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 | | http://functions.wolfram.com/07.23.03.8870.01 | 
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 | | Hypergeometric2F1[5, 17/3, -(16/3), z] == (1/(208 (-1 + z)^16)) 
  (208 - 4433 z + 47740 z^2 - 358050 z^3 + 2250600 z^4 - 14966490 z^5 + 
   239463840 z^6 + 1111796400 z^7 + 1111796400 z^8 + 324273950 z^9 + 
   23583560 z^10 + 153140 z^11) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["5", ",", FractionBox["17", "3"], ",", RowBox[List["-", FractionBox["16", "3"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["208", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "16"]]]], RowBox[List["(", RowBox[List["208", "-", RowBox[List["4433", " ", "z"]], "+", RowBox[List["47740", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["358050", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["2250600", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["14966490", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["239463840", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["1111796400", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["1111796400", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["324273950", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["23583560", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["153140", " ", SuperscriptBox["z", "11"]]]]], ")"]]]]]]]] | 
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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>  <mn> 5 </mn>  <mo> , </mo>  <mfrac>  <mn> 17 </mn>  <mn> 3 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 16 </mn>  <mn> 3 </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["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["17", "3"], 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["16", "3"]]], 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> 208 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 16 </mn>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 153140 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 11 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 23583560 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 10 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 324273950 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 9 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 1111796400 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 8 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 1111796400 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 7 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 239463840 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 14966490 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 2250600 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 358050 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 47740 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 4433 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 208 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <cn type='integer'> 5 </cn>  <cn type='rational'> 17 <sep /> 3 </cn>  </list>  <list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 16 <sep /> 3 </cn>  </apply>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 208 </cn>  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> -1 </cn>  </apply>  <cn type='integer'> 16 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 153140 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 11 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 23583560 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 10 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 324273950 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 9 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 1111796400 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 8 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 1111796400 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 7 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 239463840 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 14966490 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 2250600 </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'> 358050 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 47740 </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'> 4433 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='integer'> 208 </cn>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["5", ",", FractionBox["17", "3"], ",", RowBox[List["-", FractionBox["16", "3"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["208", "-", RowBox[List["4433", " ", "z"]], "+", RowBox[List["47740", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["358050", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["2250600", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["14966490", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["239463840", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["1111796400", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["1111796400", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["324273950", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["23583560", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["153140", " ", SuperscriptBox["z", "11"]]]]], RowBox[List["208", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "16"]]]]]]]] | 
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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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