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 | | http://functions.wolfram.com/07.23.03.0940.01 | 
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 | | Hypergeometric2F1[-(11/2), 2, 9/2, -z] == (1/(1179648 z^(7/2))) 
  (Sqrt[z] (17325 + 
     z (87780 + z (97020 + z (863244 + 11 z (153122 + 
             3 z (52284 + 7 z (4404 + 5 z (284 + 39 z)))))))) + 
   3465 (1 + z)^8 (-5 + 13 z) ArcTan[Sqrt[z]]) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", "2", ",", FractionBox["9", "2"], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["1179648", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["z"], " ", RowBox[List["(", RowBox[List["17325", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["87780", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["97020", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["863244", "+", RowBox[List["11", " ", "z", " ", RowBox[List["(", RowBox[List["153122", "+", RowBox[List["3", " ", "z", " ", RowBox[List["(", RowBox[List["52284", "+", RowBox[List["7", " ", "z", " ", RowBox[List["(", RowBox[List["4404", "+", RowBox[List["5", " ", "z", " ", RowBox[List["(", RowBox[List["284", "+", RowBox[List["39", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["3465", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["13", " ", "z"]]]], ")"]], " ", RowBox[List["ArcTan", "[", SqrtBox["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>  <mn> 2 </mn>  </mrow>  <mo> ; </mo>  <mfrac>  <mn> 9 </mn>  <mn> 2 </mn>  </mfrac>  <mo> ; </mo>  <mrow>  <mo> - </mo>  <mi> z </mi>  </mrow>  </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["2", Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["9", "2"], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "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> 1179648 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 7 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 3465 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 13 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 5 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msup>  <mi> tan </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>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 8 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <msqrt>  <mi> z </mi>  </msqrt>  <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> 11 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 3 </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> 5 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 39 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 284 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 4404 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 52284 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 153122 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 863244 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 97020 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 87780 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 17325 </mn>  </mrow>  <mo> ) </mo>  </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='integer'> 2 </cn>  <cn type='rational'> 9 <sep /> 2 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 1179648 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 7 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 3465 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 13 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> -5 </cn>  </apply>  <apply>  <times />  <apply>  <power />  <ci> tan </ci>  <cn type='integer'> -1 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> 1 </cn>  </apply>  <cn type='integer'> 8 </cn>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </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'> 11 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 3 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 7 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 5 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 39 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 284 </cn>  </apply>  </apply>  <cn type='integer'> 4404 </cn>  </apply>  </apply>  <cn type='integer'> 52284 </cn>  </apply>  </apply>  <cn type='integer'> 153122 </cn>  </apply>  </apply>  <cn type='integer'> 863244 </cn>  </apply>  </apply>  <cn type='integer'> 97020 </cn>  </apply>  </apply>  <cn type='integer'> 87780 </cn>  </apply>  </apply>  <cn type='integer'> 17325 </cn>  </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"]]], ",", "2", ",", FractionBox["9", "2"], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[SqrtBox["z"], " ", RowBox[List["(", RowBox[List["17325", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["87780", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["97020", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["863244", "+", RowBox[List["11", " ", "z", " ", RowBox[List["(", RowBox[List["153122", "+", RowBox[List["3", " ", "z", " ", RowBox[List["(", RowBox[List["52284", "+", RowBox[List["7", " ", "z", " ", RowBox[List["(", RowBox[List["4404", "+", RowBox[List["5", " ", "z", " ", RowBox[List["(", RowBox[List["284", "+", RowBox[List["39", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["3465", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["13", " ", "z"]]]], ")"]], " ", RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]]]]]], RowBox[List["1179648", " ", SuperscriptBox["z", RowBox[List["7", "/", "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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