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http://functions.wolfram.com/07.23.03.0714.01
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Hypergeometric2F1[-(11/2), -(11/2), 4, z] ==
(1/(846170325 Pi z^3))
(32
((1848 + z (-66297 + z (1861167 + z (150642451 +
z (837650075 + z (1298925301 + z (660276301 + z (101130929 +
3031537 z)))))))) EllipticE[z] +
(-1 + z) (1848 + z (-65373 + z (1828827 +
z (98659135 + z (474147415 + z (639000201 + z (277530769 +
z (34858069 + 765765 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"]]], ",", "4", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["846170325", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], RowBox[List["(", RowBox[List["32", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1848", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "66297"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1861167", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["150642451", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["837650075", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1298925301", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["660276301", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["101130929", "+", RowBox[List["3031537", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["1848", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "65373"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1828827", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["98659135", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["474147415", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["639000201", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["277530769", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["34858069", "+", RowBox[List["765765", " ", "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> 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["11", "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> 846170325 </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> 3031537 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 101130929 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 660276301 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1298925301 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 837650075 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 150642451 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1861167 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 66297 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1848 </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> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 765765 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 34858069 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 277530769 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 639000201 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 474147415 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 98659135 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1828827 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 65373 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1848 </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'> 4 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 846170325 </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'> 3031537 </cn> <ci> z </ci> </apply> <cn type='integer'> 101130929 </cn> </apply> </apply> <cn type='integer'> 660276301 </cn> </apply> </apply> <cn type='integer'> 1298925301 </cn> </apply> </apply> <cn type='integer'> 837650075 </cn> </apply> </apply> <cn type='integer'> 150642451 </cn> </apply> </apply> <cn type='integer'> 1861167 </cn> </apply> </apply> <cn type='integer'> -66297 </cn> </apply> </apply> <cn type='integer'> 1848 </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 /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 765765 </cn> <ci> z </ci> </apply> <cn type='integer'> 34858069 </cn> </apply> </apply> <cn type='integer'> 277530769 </cn> </apply> </apply> <cn type='integer'> 639000201 </cn> </apply> </apply> <cn type='integer'> 474147415 </cn> </apply> </apply> <cn type='integer'> 98659135 </cn> </apply> </apply> <cn type='integer'> 1828827 </cn> </apply> </apply> <cn type='integer'> -65373 </cn> </apply> </apply> <cn type='integer'> 1848 </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["11", "2"]]], ",", "4", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1848", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "66297"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1861167", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["150642451", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["837650075", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1298925301", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["660276301", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["101130929", "+", RowBox[List["3031537", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["1848", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "65373"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1828827", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["98659135", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["474147415", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["639000201", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["277530769", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["34858069", "+", RowBox[List["765765", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "z", "]"]]]]]], ")"]]]], RowBox[List["846170325", " ", "\[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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