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http://functions.wolfram.com/07.23.03.1100.01
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Hypergeometric2F1[-(11/2), 11/2, 5, z] ==
-((1/(72747675 Pi z^4))
(256
((176 + z (880 + z (4675 + z (40106 + z (-1480805 + 8 z (841771 +
16 z (-102455 + 128 z (795 - 398 z + 80 z^2))))))))
EllipticE[z] - 4 (-1 + z)
(-44 + z (-242 + z (-1298 + z (-10725 + z (222485 + 16 z (-46897 +
32 z (2047 + 32 z (-41 + 10 z)))))))) EllipticK[z])))
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", FractionBox["11", "2"], ",", "5", ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List["72747675", " ", "\[Pi]", " ", SuperscriptBox["z", "4"]]]], RowBox[List["(", RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["176", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["880", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["4675", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["40106", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1480805"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["841771", "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "102455"]], "+", RowBox[List["128", " ", "z", " ", RowBox[List["(", RowBox[List["795", "-", RowBox[List["398", " ", "z"]], "+", RowBox[List["80", " ", SuperscriptBox["z", "2"]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "44"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "242"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1298"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "10725"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["222485", "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "46897"]], "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List["2047", "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "41"]], "+", RowBox[List["10", " ", "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> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mn> 5 </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["11", "2"], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["5", 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> 72747675 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 256 </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> <mn> 8 </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> 128 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 80 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 398 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 795 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 102455 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 841771 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1480805 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 40106 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 4675 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 880 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 176 </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> <mn> 4 </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> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <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> 32 </mn> <mo> ⁢ </mo> <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> 10 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 41 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2047 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 46897 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 222485 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 10725 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1298 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 242 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 44 </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> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <cn type='rational'> 11 <sep /> 2 </cn> <cn type='integer'> 5 </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'> 72747675 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 256 </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 /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 128 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 80 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 398 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 795 </cn> </apply> </apply> <cn type='integer'> -102455 </cn> </apply> </apply> <cn type='integer'> 841771 </cn> </apply> </apply> <cn type='integer'> -1480805 </cn> </apply> </apply> <cn type='integer'> 40106 </cn> </apply> </apply> <cn type='integer'> 4675 </cn> </apply> </apply> <cn type='integer'> 880 </cn> </apply> </apply> <cn type='integer'> 176 </cn> </apply> <apply> <times /> <exponentiale /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </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 /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 32 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 32 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> z </ci> </apply> <cn type='integer'> -41 </cn> </apply> </apply> <cn type='integer'> 2047 </cn> </apply> </apply> <cn type='integer'> -46897 </cn> </apply> </apply> <cn type='integer'> 222485 </cn> </apply> </apply> <cn type='integer'> -10725 </cn> </apply> </apply> <cn type='integer'> -1298 </cn> </apply> </apply> <cn type='integer'> -242 </cn> </apply> </apply> <cn type='integer'> -44 </cn> </apply> <apply> <times /> <ci> K </ci> <ci> z </ci> </apply> </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[RowBox[List["-", FractionBox["11", "2"]]], ",", FractionBox["11", "2"], ",", "5", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["176", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["880", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["4675", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["40106", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1480805"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["841771", "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "102455"]], "+", RowBox[List["128", " ", "z", " ", RowBox[List["(", RowBox[List["795", "-", RowBox[List["398", " ", "z"]], "+", RowBox[List["80", " ", SuperscriptBox["z", "2"]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "44"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "242"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1298"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "10725"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["222485", "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "46897"]], "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List["2047", "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "41"]], "+", RowBox[List["10", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "z", "]"]]]]]], ")"]]]], RowBox[List["72747675", " ", "\[Pi]", " ", SuperscriptBox["z", "4"]]]]]]]]]] |
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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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