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http://functions.wolfram.com/07.23.03.0770.01
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Hypergeometric2F1[-(11/2), -(7/2), 5, z] == (1/(945719775 Pi z^4))
(256
(2 (-56 + z (1316 + z (-18046 + z (248185 + z (9343280 + z (25310443 +
z (16931002 + z (2686623 - 455 (-52 + z) z))))))))
EllipticE[z] + (-1 + z) (-112 +
z (2576 + z (-34825 + z (479430 + z (11531545 + z (26180836 +
z (14570617 + 455 z (3946 + z)))))))) EllipticK[z]))
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", FractionBox["7", "2"]]], ",", "5", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["945719775", " ", "\[Pi]", " ", SuperscriptBox["z", "4"]]]], RowBox[List["(", RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "56"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1316", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "18046"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["248185", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["9343280", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["25310443", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["16931002", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2686623", "-", RowBox[List["455", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "52"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "112"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2576", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "34825"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["479430", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["11531545", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["26180836", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["14570617", "+", RowBox[List["455", " ", "z", " ", RowBox[List["(", RowBox[List["3946", "+", "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> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> </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[RowBox[List["-", FractionBox["7", "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> 945719775 </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> <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> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2686623 </mn> <mo> - </mo> <mrow> <mn> 455 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 52 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 16931002 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 25310443 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 9343280 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 248185 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 18046 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1316 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 56 </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> 455 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 3946 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 14570617 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 26180836 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 11531545 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 479430 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 34825 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2576 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 112 </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'> 7 <sep /> 2 </cn> </apply> <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'> 945719775 </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 /> <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 /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <cn type='integer'> 2686623 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 455 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -52 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='integer'> 16931002 </cn> </apply> </apply> <cn type='integer'> 25310443 </cn> </apply> </apply> <cn type='integer'> 9343280 </cn> </apply> </apply> <cn type='integer'> 248185 </cn> </apply> </apply> <cn type='integer'> -18046 </cn> </apply> </apply> <cn type='integer'> 1316 </cn> </apply> </apply> <cn type='integer'> -56 </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'> 455 </cn> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 3946 </cn> </apply> </apply> <cn type='integer'> 14570617 </cn> </apply> </apply> <cn type='integer'> 26180836 </cn> </apply> </apply> <cn type='integer'> 11531545 </cn> </apply> </apply> <cn type='integer'> 479430 </cn> </apply> </apply> <cn type='integer'> -34825 </cn> </apply> </apply> <cn type='integer'> 2576 </cn> </apply> </apply> <cn type='integer'> -112 </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["7", "2"]]], ",", "5", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "56"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1316", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "18046"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["248185", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["9343280", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["25310443", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["16931002", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2686623", "-", RowBox[List["455", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "52"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "112"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2576", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "34825"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["479430", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["11531545", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["26180836", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["14570617", "+", RowBox[List["455", " ", "z", " ", RowBox[List["(", RowBox[List["3946", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "z", "]"]]]]]], ")"]]]], RowBox[List["945719775", " ", "\[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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