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http://functions.wolfram.com/07.23.03.1205.01
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Hypergeometric2F1[-(9/2), -(5/2), 5, z] == (1/(109504395 Pi z^4))
(256
(2 (-24 + z (436 + z (-4451 + z (43362 + z (985343 + z (1459088 +
z (394539 - 143 (-38 + z) z))))))) EllipticE[z] +
(-1 + z) (-48 +
z (848 + z (-8487 + z (82635 + z (1154986 + z (1371654 +
143 z (1971 + z))))))) EllipticK[z]))
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]], ",", "5", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["109504395", " ", "\[Pi]", " ", SuperscriptBox["z", "4"]]]], RowBox[List["(", RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["436", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4451"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["43362", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["985343", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1459088", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["394539", "-", RowBox[List["143", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "38"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "48"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["848", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "8487"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["82635", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1154986", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1371654", "+", RowBox[List["143", " ", "z", " ", RowBox[List["(", RowBox[List["1971", "+", "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> <mrow> <mo> - </mo> <mfrac> <mn> 5 </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["9", "2"]]], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", 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["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> 109504395 </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> <mn> 394539 </mn> <mo> - </mo> <mrow> <mn> 143 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 38 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1459088 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 985343 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 43362 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 4451 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 436 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 24 </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> <mn> 143 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1971 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1371654 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1154986 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 82635 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 8487 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 848 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 48 </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> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 5 <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'> 109504395 </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 /> <cn type='integer'> 394539 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 143 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -38 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='integer'> 1459088 </cn> </apply> </apply> <cn type='integer'> 985343 </cn> </apply> </apply> <cn type='integer'> 43362 </cn> </apply> </apply> <cn type='integer'> -4451 </cn> </apply> </apply> <cn type='integer'> 436 </cn> </apply> </apply> <cn type='integer'> -24 </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 /> <cn type='integer'> 143 </cn> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1971 </cn> </apply> </apply> <cn type='integer'> 1371654 </cn> </apply> </apply> <cn type='integer'> 1154986 </cn> </apply> </apply> <cn type='integer'> 82635 </cn> </apply> </apply> <cn type='integer'> -8487 </cn> </apply> </apply> <cn type='integer'> 848 </cn> </apply> </apply> <cn type='integer'> -48 </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["9", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]], ",", "5", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["436", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4451"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["43362", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["985343", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1459088", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["394539", "-", RowBox[List["143", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "38"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "48"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["848", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "8487"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["82635", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1154986", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1371654", "+", RowBox[List["143", " ", "z", " ", RowBox[List["(", RowBox[List["1971", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "z", "]"]]]]]], ")"]]]], RowBox[List["109504395", " ", "\[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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