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variants of this functions
JacobiP




Mathematica Notation

Traditional Notation









Polynomials > JacobiP[n,a,b,z] > General characteristics > Domain and analyticity





http://functions.wolfram.com/05.06.04.0001.01









  


  








Input Form





DomainAndRange[Function[{n, a, b, z}, JacobiP[n, a, b, z]]] == ProductSet[NonNegativeIntegers, Complexes, Complexes, Complexes] \[LongRightArrow] Complexes








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List["n", ",", "a", ",", "b", ",", "z"]], "}"]], ",", RowBox[List["JacobiP", "[", RowBox[List["n", ",", "a", ",", "b", ",", "z"]], "]"]]]], "]"]], "]"]], " ", "\[Equal]", "\[IndentingNewLine]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["NonNegativeIntegers", ",", "Complexes", ",", "Complexes", ",", "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> <mi> a </mi> <mo> &#8902; </mo> <mi> b </mi> <mo> &#8902; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <mrow> <msubsup> <mi> P </mi> <mi> n </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> </mrow> <mo> &#8759; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#8469; </mi> <mo> &#8855; </mo> <mi> &#8450; </mi> <mo> &#8855; </mo> <mi> &#8450; </mi> <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> <ci> a </ci> <ci> b </ci> <ci> z </ci> </apply> <apply> <ci> JacobiP </ci> <ci> n </ci> <ci> a </ci> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <ci> LongRightArrow </ci> <apply> <ci> CircleTimes </ci> <ci> &#8469; </ci> <ci> &#8450; </ci> <ci> &#8450; </ci> <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_", ",", "a_", ",", "b_", ",", "z_"]], "}"]], ",", RowBox[List["JacobiP", "[", RowBox[List["n_", ",", "a_", ",", "b_", ",", "z_"]], "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["NonNegativeIntegers", ",", "Complexes", ",", "Complexes", ",", "Complexes"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]


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





2001-10-29