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http://functions.wolfram.com/07.23.03.1366.01
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Hypergeometric2F1[-(9/2), 5/2, 4, z] == (1/(45045 Pi z^3))
(32
(
(168 + z (-273 + z (-567 + z (6049 + z (-12449 + 32 z (369 +
4 z (-43 + 8 z))))))) EllipticE[z] -
(-1 + z) (-168 +
z (189 + z (630 + z (-2899 + 8 z (489 + 32 z (-9 + 2 z))))))
EllipticK[z]))
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", FractionBox["5", "2"], ",", "4", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["45045", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], RowBox[List["(", RowBox[List["32", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["168", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "273"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "567"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["6049", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "12449"]], "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List["369", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "43"]], "+", RowBox[List["8", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "168"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["189", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["630", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2899"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["489", "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "9"]], "+", RowBox[List["2", " ", "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> 9 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mn> 4 </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["9", "2"]]], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "2"], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["4", 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> 45045 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 32 </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> 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> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 43 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 369 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 12449 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 6049 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 567 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 273 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 168 </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> <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> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 9 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 489 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 2899 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 630 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 189 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 168 </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'> 9 <sep /> 2 </cn> </apply> <cn type='rational'> 5 <sep /> 2 </cn> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 45045 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 32 </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'> 32 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> </apply> <cn type='integer'> -43 </cn> </apply> </apply> <cn type='integer'> 369 </cn> </apply> </apply> <cn type='integer'> -12449 </cn> </apply> </apply> <cn type='integer'> 6049 </cn> </apply> </apply> <cn type='integer'> -567 </cn> </apply> </apply> <cn type='integer'> -273 </cn> </apply> </apply> <cn type='integer'> 168 </cn> </apply> <apply> <times /> <exponentiale /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <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 /> <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'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -9 </cn> </apply> </apply> <cn type='integer'> 489 </cn> </apply> </apply> <cn type='integer'> -2899 </cn> </apply> </apply> <cn type='integer'> 630 </cn> </apply> </apply> <cn type='integer'> 189 </cn> </apply> </apply> <cn type='integer'> -168 </cn> </apply> <apply> <times /> <ci> K </ci> <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["9", "2"]]], ",", FractionBox["5", "2"], ",", "4", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["168", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "273"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "567"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["6049", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "12449"]], "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List["369", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "43"]], "+", RowBox[List["8", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "168"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["189", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["630", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2899"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["489", "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "9"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "z", "]"]]]]]], ")"]]]], RowBox[List["45045", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]]]]]] |
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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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