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http://functions.wolfram.com/07.23.03.1054.01
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Hypergeometric2F1[-(11/2), 9/2, 5, z] == (1/(72747675 Pi z^4))
(256
(-2 (792 + z (1452 + z (4422 + z (26235 + z (-707056 + z (2615531 +
128 z (-33633 + z (28957 + 256 z (-50 + 9 z)))))))))
EllipticE[z] + (-1 + z) (-1584 +
z (-3696 + z (-10989 + z (-58806 + z (813875 + 16 z (-135327 +
8 z (19629 + 32 z (-337 + 72 z)))))))) EllipticK[z]))
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", FractionBox["9", "2"], ",", "5", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["72747675", " ", "\[Pi]", " ", SuperscriptBox["z", "4"]]]], RowBox[List["(", RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["792", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1452", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["4422", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["26235", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "707056"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2615531", "+", RowBox[List["128", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "33633"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["28957", "+", RowBox[List["256", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "50"]], "+", RowBox[List["9", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1584"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3696"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "10989"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "58806"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["813875", "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "135327"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["19629", "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "337"]], "+", RowBox[List["72", " ", "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> 9 </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["9", "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> <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> <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> 8 </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> 72 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 337 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 19629 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 135327 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 813875 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 58806 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 10989 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 3696 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1584 </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> 2 </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> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <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> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 256 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 50 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 28957 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 33633 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2615531 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 707056 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 26235 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 4422 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1452 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 792 </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> <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'> 9 <sep /> 2 </cn> <cn type='integer'> 5 </cn> <ci> z </ci> </apply> <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 /> <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'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 32 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 72 </cn> <ci> z </ci> </apply> <cn type='integer'> -337 </cn> </apply> </apply> <cn type='integer'> 19629 </cn> </apply> </apply> <cn type='integer'> -135327 </cn> </apply> </apply> <cn type='integer'> 813875 </cn> </apply> </apply> <cn type='integer'> -58806 </cn> </apply> </apply> <cn type='integer'> -10989 </cn> </apply> </apply> <cn type='integer'> -3696 </cn> </apply> </apply> <cn type='integer'> -1584 </cn> </apply> <apply> <times /> <ci> K </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </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 /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 128 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 256 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> z </ci> </apply> <cn type='integer'> -50 </cn> </apply> </apply> <cn type='integer'> 28957 </cn> </apply> </apply> <cn type='integer'> -33633 </cn> </apply> </apply> <cn type='integer'> 2615531 </cn> </apply> </apply> <cn type='integer'> -707056 </cn> </apply> </apply> <cn type='integer'> 26235 </cn> </apply> </apply> <cn type='integer'> 4422 </cn> </apply> </apply> <cn type='integer'> 1452 </cn> </apply> </apply> <cn type='integer'> 792 </cn> </apply> <apply> <times /> <exponentiale /> <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[RowBox[List["-", FractionBox["11", "2"]]], ",", FractionBox["9", "2"], ",", "5", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["792", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1452", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["4422", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["26235", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "707056"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2615531", "+", RowBox[List["128", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "33633"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["28957", "+", RowBox[List["256", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "50"]], "+", RowBox[List["9", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1584"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3696"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "10989"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "58806"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["813875", "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "135327"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["19629", "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "337"]], "+", RowBox[List["72", " ", "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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