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variants of this functions
GegenbauerC




Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,lambda,z] > General characteristics > Branch points > With respect to z





http://functions.wolfram.com/07.14.04.0012.01









  


  








Input Form





RamificationIndex[GegenbauerC[\[Nu], \[Lambda], z], z, -1] == Log /; Element[\[Lambda] - 1/2, Integers] || ( !Element[\[Lambda] - 1/2, Rationals] && !((Element[\[Nu], Integers] && \[Nu] >= 0) || (Element[-2 \[Lambda] - \[Nu], Integers] && -2 \[Lambda] - \[Nu] >= 0)))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]", ",", "\[Lambda]", ",", "z"]], "]"]], ",", "z", ",", RowBox[List["-", "1"]]]], "]"]], "\[Equal]", "Log"]], "/;", " ", RowBox[List[RowBox[List["Element", "[", RowBox[List[RowBox[List["\[Lambda]", "-", FractionBox["1", "2"]]], ",", "Integers"]], "]"]], "\[Or]", RowBox[List[RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List[RowBox[List["\[Lambda]", "-", FractionBox["1", "2"]]], ",", "Rationals"]], "]"]], "]"]], "\[And]", RowBox[List["Not", "[", RowBox[List[RowBox[List[RowBox[List["Element", "[", RowBox[List["\[Nu]", ",", "Integers"]], "]"]], "\[And]", RowBox[List["\[Nu]", "\[GreaterEqual]", "0"]]]], "\[Or]", RowBox[List[RowBox[List["Element", "[", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[Lambda]"]], "-", "\[Nu]"]], ",", "Integers"]], "]"]], "\[And]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[Lambda]"]], "-", "\[Nu]"]], "\[GreaterEqual]", "0"]]]]]], "]"]]]]]]]]]]








MathML Form







<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> &#8475; </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <semantics> <mrow> <msubsup> <mi> C </mi> <mi> &#957; </mi> <mi> &#955; </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[&quot;C&quot;, &quot;\[Nu]&quot;, &quot;\[Lambda]&quot;], &quot;(&quot;, &quot;z&quot;, &quot;)&quot;]], Fibonacci] </annotation> </semantics> <mo> , </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mi> log </mi> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> &#955; </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mrow> <mi> &#955; </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8713; </mo> <semantics> <mi> &#8474; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalQ]&quot;, Function[Rationals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mo> &#172; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#957; </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#8475; </ci> <ci> z </ci> </apply> <apply> <ci> Fibonacci </ci> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> C </ci> <ci> &#957; </ci> </apply> <ci> &#955; </ci> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <ci> log </ci> </apply> <apply> <or /> <apply> <in /> <apply> <plus /> <ci> &#955; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <integers /> </apply> <apply> <and /> <apply> <notin /> <apply> <plus /> <ci> &#955; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <rationals /> </apply> <apply> <not /> <apply> <or /> <apply> <in /> <ci> &#957; </ci> <ci> &#8469; </ci> </apply> <apply> <in /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> &#955; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <ci> &#8469; </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]_", ",", "\[Lambda]_", ",", "z_"]], "]"]], ",", "z_", ",", RowBox[List["-", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Log", "/;", RowBox[List[RowBox[List[RowBox[List["\[Lambda]", "-", FractionBox["1", "2"]]], "\[Element]", "Integers"]], "||", RowBox[List["(", RowBox[List[RowBox[List["!", RowBox[List[RowBox[List["\[Lambda]", "-", FractionBox["1", "2"]]], "\[Element]", "Rationals"]]]], "&&", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[Nu]", "\[Element]", "Integers"]], "&&", RowBox[List["\[Nu]", "\[GreaterEqual]", "0"]]]], ")"]], "||", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[Lambda]"]], "-", "\[Nu]"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[Lambda]"]], "-", "\[Nu]"]], "\[GreaterEqual]", "0"]]]], ")"]]]], ")"]]]]]], ")"]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29