| |  
 |  | 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | http://functions.wolfram.com/07.23.03.c8cc.01 | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | Hypergeometric2F1[21/8, 21/4, -(35/8), z] == (1/(11115 (1 - z)^(49/4))) 
  (11115 - 171171 z + 1312311 z^2 - 7022015 z^3 + 33833345 z^4 - 
   304500105 z^5 - 751100259 z^6 - 239361621 z^7) | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["21", "8"], ",", FractionBox["21", "4"], ",", RowBox[List["-", FractionBox["35", "8"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["11115", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["49", "/", "4"]]]]]], RowBox[List["(", RowBox[List["11115", "-", RowBox[List["171171", " ", "z"]], "+", RowBox[List["1312311", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["7022015", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["33833345", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["304500105", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["751100259", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["239361621", " ", SuperscriptBox["z", "7"]]]]], ")"]]]]]]]] | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 | | 
   <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>  <mfrac>  <mn> 21 </mn>  <mn> 8 </mn>  </mfrac>  <mo> , </mo>  <mfrac>  <mn> 21 </mn>  <mn> 4 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 35 </mn>  <mn> 8 </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[FractionBox["21", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["21", "4"], 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["35", "8"]]], 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> 11115 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 49 </mn>  <mo> / </mo>  <mn> 4 </mn>  </mrow>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mn> 239361621 </mn>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 7 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 751100259 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 304500105 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 33833345 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 7022015 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 1312311 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 171171 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 11115 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <cn type='rational'> 21 <sep /> 8 </cn>  <cn type='rational'> 21 <sep /> 4 </cn>  </list>  <list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 35 <sep /> 8 </cn>  </apply>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 11115 </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'> 49 <sep /> 4 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -239361621 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 7 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 751100259 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 304500105 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 33833345 </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'> 7022015 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 1312311 </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'> 171171 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='integer'> 11115 </cn>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   | 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  |  
 |  
 |  
 |  |  
 |  |  
 |  |  
 |  
 |  
 |  |  
 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["21", "8"], ",", FractionBox["21", "4"], ",", RowBox[List["-", FractionBox["35", "8"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["11115", "-", RowBox[List["171171", " ", "z"]], "+", RowBox[List["1312311", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["7022015", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["33833345", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["304500105", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["751100259", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["239361621", " ", SuperscriptBox["z", "7"]]]]], RowBox[List["11115", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["49", "/", "4"]]]]]]]]]] | 
 |  
 |   
 |  
 |  
 | |   
 |  
 |  
 |  
 |  
 |  
 |  
 | | Date Added to functions.wolfram.com (modification date) | 
 |  
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |   
 |  
 |  
 |  |  | 
 | | 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] |  |  | 
 | 
 
 | 
 |