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http://functions.wolfram.com/07.23.03.c67o.01
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Hypergeometric2F1[17/8, 21/8, -(11/2), -z] == (1/(135168 (1 + z)^(81/8)))
((135168 + 1501440 z + 7760480 z^2 + 25090117 z^3 + 58674135 z^4 +
116133498 z^5 + 323691030 z^6 - 255723775 z^7 + 10407027 z^8)
Cos[ArcTan[Sqrt[z]]/4] + 2 Sqrt[z] (16896 + 182400 z + 914446 z^2 +
2864745 z^3 + 6506760 z^4 + 12684126 z^5 - 208415230 z^6 + 40124881 z^7)
Sin[ArcTan[Sqrt[z]]/4])
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["17", "8"], ",", FractionBox["21", "8"], ",", RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["135168", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["81", "/", "8"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["135168", "+", RowBox[List["1501440", " ", "z"]], "+", RowBox[List["7760480", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["25090117", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["58674135", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["116133498", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["323691030", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["255723775", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["10407027", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]], "4"], "]"]]]], "+", RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["16896", "+", RowBox[List["182400", " ", "z"]], "+", RowBox[List["914446", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2864745", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["6506760", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["12684126", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["208415230", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["40124881", " ", SuperscriptBox["z", "7"]]]]], ")"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]], "4"], "]"]]]]]], ")"]]]]]]]]
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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> <mfrac> <mn> 17 </mn> <mn> 8 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 21 </mn> <mn> 8 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <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[FractionBox["17", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["21", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["11", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "z"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] </annotation> </semantics> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 135168 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 81 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 10407027 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 255723775 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 323691030 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 116133498 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 58674135 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 25090117 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7760480 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1501440 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 135168 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 40124881 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 208415230 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 12684126 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6506760 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2864745 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 914446 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 182400 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 16896 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='rational'> 17 <sep /> 8 </cn> <cn type='rational'> 21 <sep /> 8 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </list> <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'> 135168 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 81 <sep /> 8 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 10407027 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 255723775 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 323691030 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 116133498 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 58674135 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 25090117 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7760480 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1501440 </cn> <ci> z </ci> </apply> <cn type='integer'> 135168 </cn> </apply> <apply> <cos /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <arctan /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 40124881 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 208415230 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 12684126 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6506760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2864745 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 914446 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 182400 </cn> <ci> z </ci> </apply> <cn type='integer'> 16896 </cn> </apply> <apply> <sin /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <arctan /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </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[FractionBox["17", "8"], ",", FractionBox["21", "8"], ",", RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["135168", "+", RowBox[List["1501440", " ", "z"]], "+", RowBox[List["7760480", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["25090117", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["58674135", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["116133498", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["323691030", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["255723775", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["10407027", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]], "4"], "]"]]]], "+", RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["16896", "+", RowBox[List["182400", " ", "z"]], "+", RowBox[List["914446", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2864745", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["6506760", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["12684126", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["208415230", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["40124881", " ", SuperscriptBox["z", "7"]]]]], ")"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]], "4"], "]"]]]]]], RowBox[List["135168", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["81", "/", "8"]]]]]]]]]] |
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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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