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variants of this functions
JacobiP






Mathematica Notation

Traditional Notation









Hypergeometric Functions > JacobiP[nu,a,b,z] > Specific values > Specialized values > For fixed a,b,z





http://functions.wolfram.com/07.15.03.0017.01









  


  










Input Form





JacobiP[3, a, b, z] == (1/48) ((a - b) (-16 + a^2 + (-3 + b) b - a (3 + 2 b)) + 3 (4 + a + b) (-6 + a^2 - b + b^2 - a (1 + 2 b)) z + 3 (a - b) (4 + a + b) (5 + a + b) z^2 + (4 + a + b) (5 + a + b) (6 + a + b) z^3)










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["JacobiP", "[", RowBox[List["3", ",", "a", ",", "b", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "48"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "16"]], "+", SuperscriptBox["a", "2"], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "b"]], ")"]], " ", "b"]], "-", RowBox[List["a", " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "b"]]]], ")"]]]]]], ")"]]]], "+", " ", RowBox[List["3", " ", RowBox[List["(", RowBox[List["4", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6"]], "+", SuperscriptBox["a", "2"], "-", "b", "+", SuperscriptBox["b", "2"], "-", RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "b"]]]], ")"]]]]]], ")"]], " ", "z"]], "+", " ", RowBox[List["3", " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["5", "+", "a", "+", "b"]], ")"]], " ", SuperscriptBox["z", "2"]]], "+", " ", RowBox[List[RowBox[List["(", RowBox[List["4", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["5", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["6", "+", "a", "+", "b"]], ")"]], " ", SuperscriptBox["z", "3"]]]]], ")"]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msubsup> <mi> P </mi> <mn> 3 </mn> <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> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 48 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mi> b </mi> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiP", "[", RowBox[List["3", ",", "a_", ",", "b_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "48"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "16"]], "+", SuperscriptBox["a", "2"], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "b"]], ")"]], " ", "b"]], "-", RowBox[List["a", " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "b"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["3", " ", RowBox[List["(", RowBox[List["4", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6"]], "+", SuperscriptBox["a", "2"], "-", "b", "+", SuperscriptBox["b", "2"], "-", RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "b"]]]], ")"]]]]]], ")"]], " ", "z"]], "+", RowBox[List["3", " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["5", "+", "a", "+", "b"]], ")"]], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["4", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["5", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["6", "+", "a", "+", "b"]], ")"]], " ", SuperscriptBox["z", "3"]]]]], ")"]]]]]]]]










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





2001-10-29





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