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http://functions.wolfram.com/07.27.04.0015.01
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RamificationIndex[HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2],
Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z], z,
ComplexInfinity] == Log /; Exists[Subscript[a, i], Subscript[a, j],
Element[Subscript[a, i] - Subscript[a, j], Integers] && 1 <= i <= 3 &&
1 <= j <= 3 && i != j] && ( !Element[Subscript[a, 1], Rationals] ||
!Element[Subscript[a, 2], Rationals] ||
!Element[Subscript[a, 3], Rationals])
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", SubscriptBox["a", "2"], ",", SubscriptBox["a", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"]]], "}"]], ",", "z"]], "]"]], ",", "z", ",", "ComplexInfinity"]], "]"]], "\[Equal]", "Log"]], "/;", RowBox[List[RowBox[List[SubscriptBox["\[Exists]", RowBox[List[SubscriptBox["a", "i"], ",", SubscriptBox["a", "j"]]]], RowBox[List["(", RowBox[List[RowBox[List["Element", "[", RowBox[List[RowBox[List[SubscriptBox["a", "i"], "-", SubscriptBox["a", "j"]]], ",", "Integers"]], "]"]], "\[And]", RowBox[List["1", "\[LessEqual]", "i", "\[LessEqual]", "3"]], "\[And]", RowBox[List["1", "\[LessEqual]", "j", "\[LessEqual]", "3"]], "\[And]", RowBox[List["i", "\[NotEqual]", "j"]]]], ")"]]]], "\[And]", RowBox[List["(", RowBox[List[RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List[SubscriptBox["a", "1"], ",", "Rationals"]], "]"]], "]"]], "\[Or]", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List[SubscriptBox["a", "2"], ",", "Rationals"]], "]"]], "]"]], "\[Or]", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List[SubscriptBox["a", "3"], ",", "Rationals"]], "]"]], "]"]]]], ")"]]]]]]]]
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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> <mrow> <msub> <mi> ℛ </mi> <mi> z </mi> </msub> <mo> ( </mo> <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> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> ; </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> 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[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], 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]] </annotation> </semantics> <mo> , </mo> <mover> <mi> ∞ </mi> <mo> ~ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mi> log </mi> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mo> ∃ </mo> <mrow> <msub> <mi> a </mi> <mi> i </mi> </msub> <mo> , </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> </msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> a </mi> <mi> i </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mn> 1 </mn> <mo> ≤ </mo> <mi> i </mi> <mo> ≤ </mo> <mn> 3 </mn> </mrow> <mo> ∧ </mo> <mrow> <mn> 1 </mn> <mo> ≤ </mo> <mi> j </mi> <mo> ≤ </mo> <mn> 3 </mn> </mrow> <mo> ∧ </mo> <mrow> <mi> i </mi> <mo> ≠ </mo> <mi> j </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ∧ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> ∉ </mo> <semantics> <mi> ℚ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalQ]", Function[Rationals]] </annotation> </semantics> </mrow> <mo> ∨ </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ∉ </mo> <semantics> <mi> ℚ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalQ]", Function[Rationals]] </annotation> </semantics> </mrow> <mo> ∨ </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> ∉ </mo> <semantics> <mi> ℚ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalQ]", Function[Rationals]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> ℛ </ci> <ci> z </ci> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </list> <ci> z </ci> </apply> <apply> <ci> OverTilde </ci> <infinity /> </apply> </apply> <ci> log </ci> </apply> <apply> <and /> <apply> <exists /> <bvar> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> i </ci> </apply> </bvar> <bvar> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> j </ci> </apply> </bvar> <apply> <and /> <apply> <in /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> i </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> j </ci> </apply> </apply> </apply> <integers /> </apply> <apply> <leq /> <cn type='integer'> 1 </cn> <ci> i </ci> <cn type='integer'> 3 </cn> </apply> <apply> <leq /> <cn type='integer'> 1 </cn> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <apply> <neq /> <ci> i </ci> <ci> j </ci> </apply> </apply> </apply> <apply> <or /> <apply> <notin /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <rationals /> </apply> <apply> <notin /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <rationals /> </apply> <apply> <notin /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <rationals /> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", SubscriptBox["a_", "2"], ",", SubscriptBox["a_", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", SubscriptBox["b_", "2"]]], "}"]], ",", "z_"]], "]"]], ",", "z_", ",", "ComplexInfinity"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Log", "/;", RowBox[List[RowBox[List[SubscriptBox["\[Exists]", RowBox[List[SubscriptBox["a", "i"], ",", SubscriptBox["a", "j"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["a", "i"], "-", SubscriptBox["a", "j"]]], "\[Element]", "Integers"]], "&&", RowBox[List["1", "\[LessEqual]", "i", "\[LessEqual]", "3"]], "&&", RowBox[List["1", "\[LessEqual]", "j", "\[LessEqual]", "3"]], "&&", RowBox[List["i", "\[NotEqual]", "j"]]]], ")"]]]], "&&", RowBox[List["(", RowBox[List[RowBox[List["!", RowBox[List[SubscriptBox["a", "1"], "\[Element]", "Rationals"]]]], "||", RowBox[List["!", RowBox[List[SubscriptBox["a", "2"], "\[Element]", "Rationals"]]]], "||", RowBox[List["!", RowBox[List[SubscriptBox["a", "3"], "\[Element]", "Rationals"]]]]]], ")"]]]]]]]]]] |
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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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