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http://functions.wolfram.com/07.23.03.0741.01
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Hypergeometric2F1[-(11/2), -(9/2), 4, z] == (1/(49774725 Pi z^3))
(32
((168 + z (-5313 + z (129213 + z (8583335 + z (38370845 + z (45093861 +
z (15607679 + z (1268021 + 4095 z)))))))) EllipticE[z] +
(-1 + z) (168 +
z (-5229 + z (126630 + z (5534765 + z (21134940 + z (21241341 +
z (6112502 + 380835 z))))))) EllipticK[z]))
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", FractionBox["9", "2"]]], ",", "4", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["49774725", " ", "\[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["-", "5313"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["129213", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8583335", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["38370845", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["45093861", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["15607679", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1268021", "+", RowBox[List["4095", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["168", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5229"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["126630", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["5534765", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["21134940", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["21241341", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["6112502", "+", RowBox[List["380835", " ", "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> 9 </mn> <mn> 2 </mn> </mfrac> </mrow> </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["11", "2"]]], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", 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["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> 49774725 </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> <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> 4095 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1268021 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 15607679 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 45093861 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 38370845 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 8583335 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 129213 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 5313 </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> <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> 380835 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 6112502 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 21241341 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 21134940 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 5534765 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 126630 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 5229 </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'> 11 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <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'> 49774725 </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 /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4095 </cn> <ci> z </ci> </apply> <cn type='integer'> 1268021 </cn> </apply> </apply> <cn type='integer'> 15607679 </cn> </apply> </apply> <cn type='integer'> 45093861 </cn> </apply> </apply> <cn type='integer'> 38370845 </cn> </apply> </apply> <cn type='integer'> 8583335 </cn> </apply> </apply> <cn type='integer'> 129213 </cn> </apply> </apply> <cn type='integer'> -5313 </cn> </apply> </apply> <cn type='integer'> 168 </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 /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 380835 </cn> <ci> z </ci> </apply> <cn type='integer'> 6112502 </cn> </apply> </apply> <cn type='integer'> 21241341 </cn> </apply> </apply> <cn type='integer'> 21134940 </cn> </apply> </apply> <cn type='integer'> 5534765 </cn> </apply> </apply> <cn type='integer'> 126630 </cn> </apply> </apply> <cn type='integer'> -5229 </cn> </apply> </apply> <cn type='integer'> 168 </cn> </apply> <apply> <times /> <ci> K </ci> <ci> z </ci> </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"]]], ",", RowBox[List["-", FractionBox["9", "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["-", "5313"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["129213", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8583335", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["38370845", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["45093861", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["15607679", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1268021", "+", RowBox[List["4095", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["168", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5229"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["126630", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["5534765", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["21134940", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["21241341", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["6112502", "+", RowBox[List["380835", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "z", "]"]]]]]], ")"]]]], RowBox[List["49774725", " ", "\[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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