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http://functions.wolfram.com/07.23.03.7788.01
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Hypergeometric2F1[1, 8/3, 14/3, z] ==
-((1/(45 z^(11/3))) (11 (-60 z^(2/3) + 36 z^(5/3) + 9 z^(8/3) +
40 (-1 + z) Log[1 - z^(1/3)] - 40 (-1)^(1/3) (-1 + z)
Log[1 + (-1)^(1/3) z^(1/3)] - 40 (-1)^(2/3)
Log[1 - (-1)^(2/3) z^(1/3)] + 40 (-1)^(2/3) z
Log[1 - (-1)^(2/3) z^(1/3)])))
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", FractionBox["8", "3"], ",", FractionBox["14", "3"], ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List["45", " ", SuperscriptBox["z", RowBox[List["11", "/", "3"]]]]]], RowBox[List["(", RowBox[List["11", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "60"]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List["36", " ", SuperscriptBox["z", RowBox[List["5", "/", "3"]]]]], "+", RowBox[List["9", " ", SuperscriptBox["z", RowBox[List["8", "/", "3"]]]]], "+", RowBox[List["40", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "]"]]]], "-", RowBox[List["40", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]]]], "]"]]]], "-", RowBox[List["40", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "3"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]]]], "]"]]]], "+", RowBox[List["40", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "3"]]], " ", "z", " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]]]
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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> <mn> 1 </mn> <mo> , </mo> <mfrac> <mn> 8 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> ; </mo> <mfrac> <mn> 14 </mn> <mn> 3 </mn> </mfrac> <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["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["8", "3"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["14", "3"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["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> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 45 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 8 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 36 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 60 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 3 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 3 </mn> </mroot> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='integer'> 1 </cn> <cn type='rational'> 8 <sep /> 3 </cn> </list> <list> <cn type='rational'> 14 <sep /> 3 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 45 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 8 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 36 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 40 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <times /> <ci> log </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> </apply> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 60 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 40 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <times /> <ci> log </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 40 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <times /> <ci> log </ci> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 40 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <times /> <ci> log </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> </apply> </apply> </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["1", ",", FractionBox["8", "3"], ",", FractionBox["14", "3"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["11", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "60"]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List["36", " ", SuperscriptBox["z", RowBox[List["5", "/", "3"]]]]], "+", RowBox[List["9", " ", SuperscriptBox["z", RowBox[List["8", "/", "3"]]]]], "+", RowBox[List["40", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "]"]]]], "-", RowBox[List["40", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]]]], "]"]]]], "-", RowBox[List["40", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "3"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]]]], "]"]]]], "+", RowBox[List["40", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "3"]]], " ", "z", " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["45", " ", SuperscriptBox["z", RowBox[List["11", "/", "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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