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   http://functions.wolfram.com/07.23.03.1003.01
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    Hypergeometric2F1[-(11/2), 7/2, 3, z] == (1/(675675 Pi z^2)) 
  (
   -16 (462 + z (5313 + z (-223428 + z (1074965 + 
           32 z (-67775 + 4 z (17247 + 56 z (-157 + 32 z))))))) 
    EllipticE[z] + 32 (-1 + z) 
    (-231 + z (-2772 + z (68055 + 4 z (-60895 + 
           16 z (5505 + 28 z (-129 + 32 z)))))) 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>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 11 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mfrac>  <mn> 7 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mn> 3 </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["11", "2"]]], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "2"], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["3", 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>  <mrow>  <mn> 675675 </mn>  <mo> ⁢ </mo>  <mi> π </mi>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 32 </mn>  <mo> ⁢ </mo>  <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>  <mn> 4 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 16 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 28 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 32 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 129 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 5505 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mn> 60895 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 68055 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mn> 2772 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mn> 231 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> K </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> - </mo>  <mrow>  <mn> 16 </mn>  <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> 32 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 56 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 32 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 157 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 17247 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mn> 67775 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 1074965 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mn> 223428 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 5313 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 462 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> E </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  </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='rational'> 7 <sep /> 2 </cn>  <cn type='integer'> 3 </cn>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 675675 </cn>  <pi />  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 32 </cn>  <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 />  <cn type='integer'> 4 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 16 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 28 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 32 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> -129 </cn>  </apply>  </apply>  <cn type='integer'> 5505 </cn>  </apply>  </apply>  <cn type='integer'> -60895 </cn>  </apply>  </apply>  <cn type='integer'> 68055 </cn>  </apply>  </apply>  <cn type='integer'> -2772 </cn>  </apply>  </apply>  <cn type='integer'> -231 </cn>  </apply>  <apply>  <times />  <ci> K </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 16 </cn>  <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'> 32 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 4 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 56 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 32 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> -157 </cn>  </apply>  </apply>  <cn type='integer'> 17247 </cn>  </apply>  </apply>  <cn type='integer'> -67775 </cn>  </apply>  </apply>  <cn type='integer'> 1074965 </cn>  </apply>  </apply>  <cn type='integer'> -223428 </cn>  </apply>  </apply>  <cn type='integer'> 5313 </cn>  </apply>  </apply>  <cn type='integer'> 462 </cn>  </apply>  <apply>  <times />  <exponentiale />  <ci> z </ci>  </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["11", "2"]]], ",", FractionBox["7", "2"], ",", "3", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "16"]], " ", RowBox[List["(", RowBox[List["462", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["5313", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "223428"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1074965", "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "67775"]], "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["17247", "+", RowBox[List["56", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "157"]], "+", RowBox[List["32", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List["32", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "231"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2772"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["68055", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "60895"]], "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List["5505", "+", RowBox[List["28", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "129"]], "+", RowBox[List["32", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "z", "]"]]]]]], RowBox[List["675675", " ", "\[Pi]", " ", SuperscriptBox["z", "2"]]]]]]]]  |  
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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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