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http://functions.wolfram.com/07.15.04.0016.01
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RamificationIndex[JacobiP[\[Nu], a, b, z], z, ComplexInfinity] == Log /;
Element[a + b + 2 \[Nu], Integers] ||
!(Element[\[Nu], Rationals] && Element[a + b + \[Nu], Rationals])
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["JacobiP", "[", RowBox[List["\[Nu]", ",", "a", ",", "b", ",", "z"]], "]"]], ",", "z", ",", "ComplexInfinity"]], "]"]], "\[Equal]", "Log"]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List[RowBox[List["a", "+", "b", "+", RowBox[List["2", "\[Nu]"]]]], ",", "Integers"]], "]"]], "\[Or]", RowBox[List["(", RowBox[List["Not", "[", RowBox[List[RowBox[List["Element", "[", RowBox[List["\[Nu]", ",", "Rationals"]], "]"]], "\[And]", RowBox[List["Element", "[", RowBox[List[RowBox[List["a", "+", "b", "+", "\[Nu]"]], ",", "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> <mrow> <msubsup> <mi> P </mi> <mi> ν </mi> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> , </mo> <mover> <mi> ∞ </mi> <mo> ~ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mi> log </mi> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </mrow> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∨ </mo> <mrow> <mo> ¬ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> ν </mi> <mo> ∈ </mo> <semantics> <mi> ℚ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalQ]", Function[Rationals]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mi> ν </mi> </mrow> <mo> ∈ </mo> <semantics> <mi> ℚ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalQ]", Function[Rationals]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> </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> JacobiP </ci> <ci> ν </ci> <ci> a </ci> <ci> b </ci> <ci> z </ci> </apply> <apply> <ci> OverTilde </ci> <infinity /> </apply> </apply> <ci> log </ci> </apply> <apply> <or /> <apply> <in /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> <integers /> </apply> <apply> <not /> <apply> <and /> <apply> <in /> <ci> ν </ci> <rationals /> </apply> <apply> <in /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <ci> ν </ci> </apply> <rationals /> </apply> </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["JacobiP", "[", RowBox[List["\[Nu]_", ",", "a_", ",", "b_", ",", "z_"]], "]"]], ",", "z_", ",", "ComplexInfinity"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Log", "/;", RowBox[List[RowBox[List[RowBox[List["a", "+", "b", "+", RowBox[List["2", " ", "\[Nu]"]]]], "\[Element]", "Integers"]], "||", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List["\[Nu]", "\[Element]", "Rationals"]], "&&", RowBox[List[RowBox[List["a", "+", "b", "+", "\[Nu]"]], "\[Element]", "Rationals"]]]], ")"]]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
