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 | | http://functions.wolfram.com/07.23.03.4483.01 | 
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 | | Hypergeometric2F1[11/2, 11/2, 2, z] == 
 -((1/(2835 Pi (-1 + z)^9 z)) 
   (4 ((35 + z (4052 + z (16434 + z (11156 + 1091 z)))) EllipticE[z] + 
     (-1 + z) (35 + z (2652 + z (8730 + z (4652 + 315 z)))) EllipticK[z]))) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["11", "2"], ",", FractionBox["11", "2"], ",", "2", ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List["2835", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "9"], " ", "z"]]], RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["35", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["4052", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["16434", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["11156", "+", RowBox[List["1091", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["35", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2652", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8730", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["4652", "+", RowBox[List["315", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "z", "]"]]]]]], ")"]]]], ")"]]]]]]]]]] | 
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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>  <mfrac>  <mn> 11 </mn>  <mn> 2 </mn>  </mfrac>  <mo> , </mo>  <mfrac>  <mn> 11 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mn> 2 </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[FractionBox["11", "2"], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "2"], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["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>  <mo> - </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mrow>  <mn> 2835 </mn>  <mo> ⁢ </mo>  <mi> π </mi>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 9 </mn>  </msup>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 1091 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 11156 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 16434 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 4052 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 35 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> E </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 315 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 4652 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 8730 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 2652 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 35 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> K </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> Hypergeometric2F1 </ci>  <cn type='rational'> 11 <sep /> 2 </cn>  <cn type='rational'> 11 <sep /> 2 </cn>  <cn type='integer'> 2 </cn>  <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'> 2835 </cn>  <pi />  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> -1 </cn>  </apply>  <cn type='integer'> 9 </cn>  </apply>  <ci> z </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 4 </cn>  <apply>  <plus />  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 1091 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 11156 </cn>  </apply>  </apply>  <cn type='integer'> 16434 </cn>  </apply>  </apply>  <cn type='integer'> 4052 </cn>  </apply>  </apply>  <cn type='integer'> 35 </cn>  </apply>  <apply>  <times />  <exponentiale />  <ci> z </ci>  </apply>  </apply>  <apply>  <times />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> -1 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 315 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 4652 </cn>  </apply>  </apply>  <cn type='integer'> 8730 </cn>  </apply>  </apply>  <cn type='integer'> 2652 </cn>  </apply>  </apply>  <cn type='integer'> 35 </cn>  </apply>  <apply>  <times />  <ci> K </ci>  <ci> z </ci>  </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[FractionBox["11", "2"], ",", FractionBox["11", "2"], ",", "2", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["35", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["4052", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["16434", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["11156", "+", RowBox[List["1091", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["35", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2652", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8730", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["4652", "+", RowBox[List["315", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "z", "]"]]]]]], ")"]]]], RowBox[List["2835", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "9"], " ", "z"]]]]]]]]] | 
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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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