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http://functions.wolfram.com/07.27.03.0502.01
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HypergeometricPFQ[{5/6, 1, 7/6}, {11/6, 13/6}, z] ==
(35/(24 z^(7/6))) (12 z^(1/6) - 2 Sqrt[3] (1 + z^(1/3))
ArcTan[1 - z^(1/3), Sqrt[3] z^(1/6)] + (-1 + z^(1/3))
(2 Log[(1 + z^(1/6))/(1 - z^(1/6))] +
Log[(1 + z^(1/6) + z^(1/3))/(1 - z^(1/6) + z^(1/3))])) /;
!IntervalMemberQ[Interval[{1, Infinity}], z]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "6"], ",", "1", ",", FractionBox["7", "6"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["11", "6"], ",", FractionBox["13", "6"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["35", RowBox[List["24", " ", SuperscriptBox["z", RowBox[List["7", "/", "6"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["12", " ", SuperscriptBox["z", RowBox[List["1", "/", "6"]]]]], "-", RowBox[List["2", " ", SqrtBox["3"], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], ",", RowBox[List[SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["1", "/", "6"]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "6"]]]]], RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "6"]]]]]], "]"]]]], "+", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "6"]]], "+", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "6"]]], "+", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]]], "]"]]]], ")"]]]]]], ")"]]]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["1", ",", "\[Infinity]"]], "}"]], "]"]], ",", " ", "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> <mrow> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 3 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 5 </mn> <mn> 6 </mn> </mfrac> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mfrac> <mn> 7 </mn> <mn> 6 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 11 </mn> <mn> 6 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 13 </mn> <mn> 6 </mn> </mfrac> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "6"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["7", "6"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["11", "6"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["13", "6"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 35 </mn> <mrow> <mn> 24 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 6 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mn> 3 </mn> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> </mrow> <mo> , </mo> <mrow> <msqrt> <mn> 3 </mn> </msqrt> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> + </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> - </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> ∉ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> ∞ </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 3 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 5 </mn> <mn> 6 </mn> </mfrac> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mfrac> <mn> 7 </mn> <mn> 6 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 11 </mn> <mn> 6 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 13 </mn> <mn> 6 </mn> </mfrac> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "6"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["7", "6"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["11", "6"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["13", "6"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 35 </mn> <mrow> <mn> 24 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 6 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mn> 3 </mn> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> </mrow> <mo> , </mo> <mrow> <msqrt> <mn> 3 </mn> </msqrt> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> + </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> - </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> ∉ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> ∞ </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "6"], ",", "1", ",", FractionBox["7", "6"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["11", "6"], ",", FractionBox["13", "6"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["35", " ", RowBox[List["(", RowBox[List[RowBox[List["12", " ", SuperscriptBox["z", RowBox[List["1", "/", "6"]]]]], "-", RowBox[List["2", " ", SqrtBox["3"], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], ",", RowBox[List[SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["1", "/", "6"]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "6"]]]]], RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "6"]]]]]], "]"]]]], "+", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "6"]]], "+", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "6"]]], "+", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]]], "]"]]]], ")"]]]]]], ")"]]]], RowBox[List["24", " ", SuperscriptBox["z", RowBox[List["7", "/", "6"]]]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["1", ",", "\[Infinity]"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]] |
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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},z] | HypergeometricPFQ[{a1,a2},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2,b3},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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