  
| 
 | 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  
  | 
  
  | 
 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  
  | 
  
  | 
 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  
  | 
  
  | 
 
 
  
  | 
  
  | 
  
  | 
 
  
  
 |  
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  | 
   http://functions.wolfram.com/07.23.03.1066.01
   |   
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  
 |  
 | 
  
  | 
 
  
  
 |  
  
  | 
  
  | 
  
  | 
 
  
  | 
    
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  | 
    Hypergeometric2F1[-(11/2), 5, -(1/2), z] == 
 (1/16384) (16384 + 
   55 z (16384 + 39 z (-9477 + 7 z (6139 + 85 z (-113 + 57 z)))) - 
   3465 z^(3/2) (1155 + 13 z (-924 + 5 z (594 + 17 z (-44 + 19 z)))) 
    ArcTanh[Sqrt[z]]) 
   |   
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  
 |  
  
  | 
  
  | 
  
  | 
 
  
  | 
    
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  | 
   Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", "5", ",", RowBox[List["-", FractionBox["1", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "16384"], RowBox[List["(", RowBox[List["16384", "+", RowBox[List["55", " ", "z", " ", RowBox[List["(", RowBox[List["16384", "+", RowBox[List["39", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "9477"]], "+", RowBox[List["7", " ", "z", " ", RowBox[List["(", RowBox[List["6139", "+", RowBox[List["85", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "113"]], "+", RowBox[List["57", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["3465", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List["1155", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "924"]], "+", RowBox[List["5", " ", "z", " ", RowBox[List["(", RowBox[List["594", "+", RowBox[List["17", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "44"]], "+", RowBox[List["19", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcTanh", "[", SqrtBox["z"], "]"]]]]]], ")"]]]]]]]] 
   |   
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  
 |  
  
  | 
  
  | 
  
  | 
 
  
  | 
    
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  
  | 
  
  | 
 
  
  | 
 
  | 
   
   <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> 11 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mn> 5 </mn>  </mrow>  <mo> ; </mo>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 1 </mn>  <mn> 2 </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["11", "2"]]], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["5", Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["1", "2"]]], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], Hypergeometric2F1] </annotation>  </semantics>  <mo>  </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mn> 16384 </mn>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mn> 3465 </mn>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 13 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 5 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 17 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 19 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 44 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 594 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mn> 924 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 1155 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msup>  <mi> tanh </mi>  <mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> ) </mo>  </mrow>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 3 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 55 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 39 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 7 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 85 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 57 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 113 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 6139 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mn> 9477 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 16384 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 16384 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> Hypergeometric2F1 </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 11 <sep /> 2 </cn>  </apply>  <cn type='integer'> 5 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='rational'> 1 <sep /> 16384 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -3465 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 13 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 5 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 17 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 19 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> -44 </cn>  </apply>  </apply>  <cn type='integer'> 594 </cn>  </apply>  </apply>  <cn type='integer'> -924 </cn>  </apply>  </apply>  <cn type='integer'> 1155 </cn>  </apply>  <apply>  <times />  <apply>  <power />  <ci> tanh </ci>  <cn type='integer'> -1 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 3 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 55 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 39 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 7 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 85 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 57 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> -113 </cn>  </apply>  </apply>  <cn type='integer'> 6139 </cn>  </apply>  </apply>  <cn type='integer'> -9477 </cn>  </apply>  </apply>  <cn type='integer'> 16384 </cn>  </apply>  <ci> z </ci>  </apply>  <cn type='integer'> 16384 </cn>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   
   |   
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
 
  |   
  |  
  |  
  |   
  |  |  
  |   
  |  
  |  
  |   
  | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", "5", ",", RowBox[List["-", FractionBox["1", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["16384", "+", RowBox[List["55", " ", "z", " ", RowBox[List["(", RowBox[List["16384", "+", RowBox[List["39", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "9477"]], "+", RowBox[List["7", " ", "z", " ", RowBox[List["(", RowBox[List["6139", "+", RowBox[List["85", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "113"]], "+", RowBox[List["57", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["3465", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List["1155", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "924"]], "+", RowBox[List["5", " ", "z", " ", RowBox[List["(", RowBox[List["594", "+", RowBox[List["17", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "44"]], "+", RowBox[List["19", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcTanh", "[", SqrtBox["z"], "]"]]]]]], "16384"]]]]]  |  
  |  
  |   
  |  
  |  
  | 
  
  
 |  
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  | 
   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] |  |   |  
  |  
  
  
  
 |  
 
 |