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variants of this functions
LegendreP




Mathematica Notation

Traditional Notation









Polynomials > LegendreP[n,mu,2,z] > General characteristics > Domain and analyticity





http://functions.wolfram.com/05.07.04.0001.01









  


  








Input Form





DomainAndRange[Function[{n, \[Mu], two, z}, LegendreP[n, \[Mu], 2, z]]] == ProductSet[NonNegativeIntegers, Complexes, {2}, Complexes] \[LongRightArrow] Complexes








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List["n", ",", " ", "\[Mu]", ",", "two", ",", "z"]], "}"]], ",", RowBox[List["LegendreP", "[", RowBox[List["n", ",", "\[Mu]", ",", "2", ",", "z"]], "]"]]]], "]"]], "]"]], " ", "\[Equal]", "\[IndentingNewLine]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["NonNegativeIntegers", ",", "Complexes", ",", RowBox[List["{", "2", "}"]], ",", "Complexes"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]








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> <mo> ( </mo> <mrow> <mi> n </mi> <mo> &#8902; </mo> <mrow> <mi> &#956; </mi> <mo> * </mo> <mn> 2 </mn> <mo> * </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <mrow> <msubsup> <semantics> <mi> P </mi> <annotation encoding='Mathematica'> TagBox[&quot;P&quot;, LegendreP] </annotation> </semantics> <mi> n </mi> <mi> &#956; </mi> </msubsup> <mo> ( </mo> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox[&quot;z&quot;, HoldComplete[LegendreP, 2]] </annotation> </semantics> <mo> ) </mo> </mrow> </mrow> <mo> &#8759; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#8469; </mi> <mo> &#8855; </mo> <mi> &#8450; </mi> <mo> &#8855; </mo> <mrow> <mo> { </mo> <mn> 2 </mn> <mo> } </mo> </mrow> <mo> &#8855; </mo> <mi> &#8450; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <mi> &#8450; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportion </ci> <apply> <ci> LongRightArrow </ci> <apply> <ci> Star </ci> <ci> n </ci> <apply> <times /> <ci> &#956; </ci> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <apply> <ci> LegendreP </ci> <ci> n </ci> <ci> &#956; </ci> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <apply> <ci> LongRightArrow </ci> <apply> <ci> CircleTimes </ci> <ci> &#8469; </ci> <ci> &#8450; </ci> <list> <cn type='integer'> 2 </cn> </list> <ci> &#8450; </ci> </apply> <ci> &#8450; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List["n_", ",", "\[Mu]_", ",", "two_", ",", "z_"]], "}"]], ",", RowBox[List["LegendreP", "[", RowBox[List["n_", ",", "\[Mu]_", ",", "2", ",", "z_"]], "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["NonNegativeIntegers", ",", "Complexes", ",", RowBox[List["{", "2", "}"]], ",", "Complexes"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]


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





2001-10-29