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http://functions.wolfram.com/07.23.03.1129.01
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Hypergeometric2F1[-(11/2), 6, 11/2, -z] == (1/(335544320 z^(9/2)))
(Sqrt[z] (-24255 +
z (112035 + z (-507276 + z (3090780 + z (288621070 +
429 z (3319570 + 7 z (960780 + 17 z (57572 + 285 z (103 +
21 z))))))))) + 3465 (1 + z)^5
(7 + 13 z (-5 + z (30 + 17 z (-10 + 19 z (5 + 21 z))))) ArcTan[Sqrt[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> <mn> 6 </mn> </mrow> <mo> ; </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> <mo> ; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </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["6", Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["11", "2"], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "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> 335544320 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3465 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 17 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 19 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 21 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 10 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 30 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <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> 429 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 17 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 285 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 21 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 103 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 57572 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 960780 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3319570 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 288621070 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3090780 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 507276 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 112035 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 24255 </mn> </mrow> <mo> ) </mo> </mrow> </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> <cn type='integer'> 6 </cn> <cn type='rational'> 11 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 335544320 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3465 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 17 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 19 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 21 </cn> <ci> z </ci> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -10 </cn> </apply> </apply> <cn type='integer'> 30 </cn> </apply> </apply> <cn type='integer'> -5 </cn> </apply> </apply> <cn type='integer'> 7 </cn> </apply> <apply> <times /> <apply> <power /> <ci> tan </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </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 /> <cn type='integer'> 429 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 17 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 285 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 21 </cn> <ci> z </ci> </apply> <cn type='integer'> 103 </cn> </apply> </apply> <cn type='integer'> 57572 </cn> </apply> </apply> <cn type='integer'> 960780 </cn> </apply> </apply> <cn type='integer'> 3319570 </cn> </apply> </apply> <cn type='integer'> 288621070 </cn> </apply> </apply> <cn type='integer'> 3090780 </cn> </apply> </apply> <cn type='integer'> -507276 </cn> </apply> </apply> <cn type='integer'> 112035 </cn> </apply> </apply> <cn type='integer'> -24255 </cn> </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"]]], ",", "6", ",", FractionBox["11", "2"], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24255"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["112035", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "507276"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["3090780", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["288621070", "+", RowBox[List["429", " ", "z", " ", RowBox[List["(", RowBox[List["3319570", "+", RowBox[List["7", " ", "z", " ", RowBox[List["(", RowBox[List["960780", "+", RowBox[List["17", " ", "z", " ", RowBox[List["(", RowBox[List["57572", "+", RowBox[List["285", " ", "z", " ", RowBox[List["(", RowBox[List["103", "+", RowBox[List["21", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["3465", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "5"], " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["30", "+", RowBox[List["17", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "10"]], "+", RowBox[List["19", " ", "z", " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["21", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]]]]]], RowBox[List["335544320", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]]]]] |
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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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