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 | | http://functions.wolfram.com/07.23.03.bnx9.01 | 
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 | | Hypergeometric2F1[-(17/8), 19/8, -(17/4), z] == 
 (2 (2288 - 6864 z + 5533 z^2 + 374 z^3 + 33 z^4 - 1364 z^5 + 672 z^6) + 
   (4576 - 16016 z + 17358 z^2 - 3355 z^3 - 1012 z^4 - 3135 z^5 + 5168 z^6 - 
     1792 z^7)/Sqrt[1 - z])/(4576 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-1 + z)^4) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["17", "8"]]], ",", FractionBox["19", "8"], ",", RowBox[List["-", FractionBox["17", "4"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["2288", "-", RowBox[List["6864", " ", "z"]], "+", RowBox[List["5533", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["374", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["33", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1364", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["672", " ", SuperscriptBox["z", "6"]]]]], ")"]]]], "+", FractionBox[RowBox[List["4576", "-", RowBox[List["16016", " ", "z"]], "+", RowBox[List["17358", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["3355", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1012", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["3135", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["5168", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["1792", " ", SuperscriptBox["z", "7"]]]]], SqrtBox[RowBox[List["1", "-", "z"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List["4576", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "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> 17 </mn>  <mn> 8 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mfrac>  <mn> 19 </mn>  <mn> 8 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 17 </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["17", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["19", "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["17", "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>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 672 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 1364 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 33 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 374 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 5533 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 6864 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 2288 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mfrac>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mn> 1792 </mn>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 7 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 5168 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 3135 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 1012 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 3355 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 17358 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 16016 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 4576 </mn>  </mrow>  <msqrt>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  </msqrt>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  <mo> / </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 4576 </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>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 4 </mn>  </msup>  </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'> 17 <sep /> 8 </cn>  </apply>  <cn type='rational'> 19 <sep /> 8 </cn>  </list>  <list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 17 <sep /> 4 </cn>  </apply>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 672 </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'> 1364 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 33 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 374 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 5533 </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'> 6864 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='integer'> 2288 </cn>  </apply>  </apply>  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -1792 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 7 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 5168 </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'> 3135 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 1012 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 3355 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 17358 </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'> 16016 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='integer'> 4576 </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>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 4576 </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>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> -1 </cn>  </apply>  <cn type='integer'> 4 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </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", "8"]]], ",", FractionBox["19", "8"], ",", RowBox[List["-", FractionBox["17", "4"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["2288", "-", RowBox[List["6864", " ", "z"]], "+", RowBox[List["5533", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["374", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["33", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1364", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["672", " ", SuperscriptBox["z", "6"]]]]], ")"]]]], "+", FractionBox[RowBox[List["4576", "-", RowBox[List["16016", " ", "z"]], "+", RowBox[List["17358", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["3355", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1012", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["3135", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["5168", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["1792", " ", SuperscriptBox["z", "7"]]]]], SqrtBox[RowBox[List["1", "-", "z"]]]]]], RowBox[List["4576", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "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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