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http://functions.wolfram.com/07.23.03.0708.01
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Hypergeometric2F1[-(11/2), -(11/2), 2, z] ==
(1/(585585 Pi z))
(4
((3465 + z (954322 + z (10460127 + z (26747804 +
z (20251831 + z (4324338 + 172673 z)))))) EllipticE[z] +
(-1 + z) (3465 + z (663262 + z (6290723 +
z (13932564 + z (8964415 + z (1557806 + 45045 z)))))) EllipticK[z]))
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", FractionBox["11", "2"]]], ",", "2", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["585585", " ", "\[Pi]", " ", "z"]]], RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["3465", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["954322", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["10460127", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["26747804", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["20251831", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["4324338", "+", RowBox[List["172673", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["3465", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["663262", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["6290723", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["13932564", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8964415", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1557806", "+", RowBox[List["45045", " ", "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> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> </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[RowBox[List["-", FractionBox["11", "2"]]], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", 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> <mfrac> <mn> 1 </mn> <mrow> <mn> 585585 </mn> <mo> ⁢ </mo> <mi> π </mi> <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> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 172673 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 4324338 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 20251831 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 26747804 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 10460127 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 954322 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3465 </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> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 45045 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1557806 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 8964415 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 13932564 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 6290723 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 663262 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3465 </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> <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> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 585585 </cn> <pi /> <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 /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 172673 </cn> <ci> z </ci> </apply> <cn type='integer'> 4324338 </cn> </apply> </apply> <cn type='integer'> 20251831 </cn> </apply> </apply> <cn type='integer'> 26747804 </cn> </apply> </apply> <cn type='integer'> 10460127 </cn> </apply> </apply> <cn type='integer'> 954322 </cn> </apply> </apply> <cn type='integer'> 3465 </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 /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 45045 </cn> <ci> z </ci> </apply> <cn type='integer'> 1557806 </cn> </apply> </apply> <cn type='integer'> 8964415 </cn> </apply> </apply> <cn type='integer'> 13932564 </cn> </apply> </apply> <cn type='integer'> 6290723 </cn> </apply> </apply> <cn type='integer'> 663262 </cn> </apply> </apply> <cn type='integer'> 3465 </cn> </apply> <apply> <times /> <ci> K </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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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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