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http://functions.wolfram.com/06.09.04.0010.01
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RamificationIndex[GammaRegularized[p/q, Subscript[z, 1], Subscript[z, 2]],
Subscript[z, k], ComplexInfinity] == q /; Element[p, Integers] &&
Element[q - 1, Integers] && q - 1 > 0 && GCD[p, q] == 1 &&
Element[k, {1, 2}]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["GammaRegularized", "[", RowBox[List[FractionBox["p", "q"], ",", SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]], ",", SubscriptBox["z", "k"], ",", "ComplexInfinity"]], "]"]], "\[Equal]", "q"]], "/;", RowBox[List[RowBox[List["p", "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["q", "-", "1"]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["q", "-", "1"]], ">", "0"]], "\[And]", RowBox[List[RowBox[List["GCD", "[", RowBox[List["p", ",", "q"]], "]"]], "\[Equal]", "1"]], "\[And]", RowBox[List["k", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2"]], "}"]]]]]]]]]]
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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> <msub> <mi> z </mi> <mi> k </mi> </msub> </msub> <mo> ( </mo> <mrow> <mrow> <semantics> <mi> Q </mi> <annotation-xml encoding='MathML-Content'> <ci> GammaRegularized </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mfrac> <mi> p </mi> <mi> q </mi> </mfrac> <mo> , </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mover> <mi> ∞ </mi> <mo> ~ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mi> q </mi> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> p </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ∈ </mo> <semantics> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> <annotation encoding='Mathematica'> TagBox[SuperscriptBox["\[DoubleStruckCapitalN]", "+"], Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mi> gcd </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> p </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mn> 1 </mn> </mrow> <mo> ∧ </mo> <mrow> <mi> k </mi> <mo> ∈ </mo> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> } </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <msub> <mi> ℛ </mi> <msub> <mi> z </mi> <mi> k </mi> </msub> </msub> <mo> ( </mo> <mrow> <mrow> <semantics> <mi> Q </mi> <annotation-xml encoding='MathML-Content'> <ci> GammaRegularized </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mfrac> <mi> p </mi> <mi> q </mi> </mfrac> <mo> , </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mover> <mi> ∞ </mi> <mo> ~ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mi> q </mi> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> p </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ∈ </mo> <semantics> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> <annotation encoding='Mathematica'> TagBox[SuperscriptBox["\[DoubleStruckCapitalN]", "+"], Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mi> gcd </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> p </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mn> 1 </mn> </mrow> <mo> ∧ </mo> <mrow> <mi> k </mi> <mo> ∈ </mo> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> } </mo> </mrow> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["GammaRegularized", "[", RowBox[List[FractionBox["p_", "q_"], ",", SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "]"]], ",", SubscriptBox["z_", "k_"], ",", "ComplexInfinity"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["q", "/;", RowBox[List[RowBox[List["p", "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["q", "-", "1"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["q", "-", "1"]], ">", "0"]], "&&", RowBox[List[RowBox[List["GCD", "[", RowBox[List["p", ",", "q"]], "]"]], "\[Equal]", "1"]], "&&", RowBox[List["k", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2"]], "}"]]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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