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 | | http://functions.wolfram.com/07.23.03.as0k.01 | 
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 | | Hypergeometric2F1[-(17/5), 1, 6, z] == 
 -((1/(1230768 z^5)) (25 (625 (-1 + (1 - z)^(2/5)) - 
     250 (-21 + 20 (1 - z)^(2/5)) z + 175 (-111 + 100 (1 - z)^(2/5)) z^2 - 
     280 (-148 + 125 (1 - z)^(2/5)) z^3 + 14 (-3996 + 3125 (1 - z)^(2/5)) 
      z^4 - 35000 (1 - z)^(2/5) z^5 + 17500 (1 - z)^(2/5) z^6 - 
     5000 (1 - z)^(2/5) z^7 + 625 (1 - z)^(2/5) z^8))) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["17", "5"]]], ",", "1", ",", "6", ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List["1230768", " ", SuperscriptBox["z", "5"]]]], RowBox[List["(", RowBox[List["25", " ", RowBox[List["(", RowBox[List[RowBox[List["625", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]], ")"]]]], "-", RowBox[List["250", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "21"]], "+", RowBox[List["20", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]]]], ")"]], " ", "z"]], "+", RowBox[List["175", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "111"]], "+", RowBox[List["100", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]]]], ")"]], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["280", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "148"]], "+", RowBox[List["125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]]]], ")"]], " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["14", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3996"]], "+", RowBox[List["3125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]]]], ")"]], " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["35000", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]], " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["17500", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]], " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["5000", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]], " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["625", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]], " ", SuperscriptBox["z", "8"]]]]], ")"]]]], ")"]]]]]]]]]] | 
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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> 17 </mn>  <mn> 5 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mn> 1 </mn>  </mrow>  <mo> ; </mo>  <mn> 6 </mn>  <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["17", "5"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["6", 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>  <mo> - </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mrow>  <mn> 1230768 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 25 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 625 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> / </mo>  <mn> 5 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 8 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 5000 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> / </mo>  <mn> 5 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 7 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 17500 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> / </mo>  <mn> 5 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 35000 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> / </mo>  <mn> 5 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 14 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 3125 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> / </mo>  <mn> 5 </mn>  </mrow>  </msup>  </mrow>  <mo> - </mo>  <mn> 3996 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 280 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 125 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> / </mo>  <mn> 5 </mn>  </mrow>  </msup>  </mrow>  <mo> - </mo>  <mn> 148 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 175 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 100 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> / </mo>  <mn> 5 </mn>  </mrow>  </msup>  </mrow>  <mo> - </mo>  <mn> 111 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 250 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 20 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> / </mo>  <mn> 5 </mn>  </mrow>  </msup>  </mrow>  <mo> - </mo>  <mn> 21 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mrow>  <mn> 625 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> / </mo>  <mn> 5 </mn>  </mrow>  </msup>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </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'> 17 <sep /> 5 </cn>  </apply>  <cn type='integer'> 1 </cn>  </list>  <list>  <cn type='integer'> 6 </cn>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 1230768 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 25 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 625 </cn>  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='rational'> 2 <sep /> 5 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 8 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 5000 </cn>  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='rational'> 2 <sep /> 5 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 7 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 17500 </cn>  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='rational'> 2 <sep /> 5 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 35000 </cn>  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='rational'> 2 <sep /> 5 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 14 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 3125 </cn>  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='rational'> 2 <sep /> 5 </cn>  </apply>  </apply>  <cn type='integer'> -3996 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 280 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 125 </cn>  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='rational'> 2 <sep /> 5 </cn>  </apply>  </apply>  <cn type='integer'> -148 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 175 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 100 </cn>  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='rational'> 2 <sep /> 5 </cn>  </apply>  </apply>  <cn type='integer'> -111 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 250 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 20 </cn>  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='rational'> 2 <sep /> 5 </cn>  </apply>  </apply>  <cn type='integer'> -21 </cn>  </apply>  <ci> z </ci>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 625 </cn>  <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'> 2 <sep /> 5 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </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["17", "5"]]], ",", "1", ",", "6", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List[RowBox[List["625", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]], ")"]]]], "-", RowBox[List["250", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "21"]], "+", RowBox[List["20", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]]]], ")"]], " ", "z"]], "+", RowBox[List["175", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "111"]], "+", RowBox[List["100", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]]]], ")"]], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["280", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "148"]], "+", RowBox[List["125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]]]], ")"]], " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["14", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3996"]], "+", RowBox[List["3125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]]]], ")"]], " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["35000", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]], " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["17500", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]], " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["5000", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]], " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["625", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]], " ", SuperscriptBox["z", "8"]]]]], ")"]]]], RowBox[List["1230768", " ", SuperscriptBox["z", "5"]]]]]]]]]] | 
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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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