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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/07.15.03.0019.01









  


  








Input Form





JacobiP[5, a, b, z] == (1/3840) (a^5 - 5 a^4 (2 + b) + 5 a^3 (-13 + 4 b + 2 b^2) - 5 a^2 (-50 - 51 b + 2 b^3) - b (1024 + 250 b - 65 b^2 - 10 b^3 + b^4) + a (1024 - 255 b^2 - 20 b^3 + 5 b^4) + 5 (6 + a + b) (240 + a^4 + 54 b - 49 b^2 - 6 b^3 + b^4 - 2 a^3 (3 + 2 b) + a^2 (-49 + 6 b + 6 b^2) + a (54 + 110 b + 6 b^2 - 4 b^3)) z + 10 (6 + a + b) (7 + a + b) (a^3 - 3 a^2 (1 + b) + b (28 + 3 b - b^2) + a (-28 + 3 b^2)) z^2 + 10 (6 + a + b) (7 + a + b) (8 + a + b) (-10 + a^2 - b + b^2 - a (1 + 2 b)) z^3 + 5 (a - b) (6 + a + b) (7 + a + b) (8 + a + b) (9 + a + b) z^4 + (6 + a + b) (7 + a + b) (8 + a + b) (9 + a + b) (10 + a + b) z^5)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["JacobiP", "[", RowBox[List["5", ",", "a", ",", "b", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "3840"], RowBox[List["(", RowBox[List[SuperscriptBox["a", "5"], "-", RowBox[List["5", " ", SuperscriptBox["a", "4"], " ", RowBox[List["(", RowBox[List["2", "+", "b"]], ")"]]]], "+", RowBox[List["5", " ", SuperscriptBox["a", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "13"]], "+", RowBox[List["4", " ", "b"]], "+", RowBox[List["2", " ", SuperscriptBox["b", "2"]]]]], ")"]]]], "-", RowBox[List["5", " ", SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "50"]], "-", RowBox[List["51", " ", "b"]], "+", RowBox[List["2", " ", SuperscriptBox["b", "3"]]]]], ")"]]]], "-", RowBox[List["b", " ", RowBox[List["(", RowBox[List["1024", "+", RowBox[List["250", " ", "b"]], "-", RowBox[List["65", " ", SuperscriptBox["b", "2"]]], "-", RowBox[List["10", " ", SuperscriptBox["b", "3"]]], "+", SuperscriptBox["b", "4"]]], ")"]]]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List["1024", "-", RowBox[List["255", " ", SuperscriptBox["b", "2"]]], "-", RowBox[List["20", " ", SuperscriptBox["b", "3"]]], "+", RowBox[List["5", " ", SuperscriptBox["b", "4"]]]]], ")"]]]], "+", RowBox[List["5", " ", RowBox[List["(", RowBox[List["6", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["240", "+", SuperscriptBox["a", "4"], "+", RowBox[List["54", " ", "b"]], "-", RowBox[List["49", " ", SuperscriptBox["b", "2"]]], "-", RowBox[List["6", " ", SuperscriptBox["b", "3"]]], "+", SuperscriptBox["b", "4"], "-", RowBox[List["2", " ", SuperscriptBox["a", "3"], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "b"]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "49"]], "+", RowBox[List["6", " ", "b"]], "+", RowBox[List["6", " ", SuperscriptBox["b", "2"]]]]], ")"]]]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List["54", "+", RowBox[List["110", " ", "b"]], "+", RowBox[List["6", " ", SuperscriptBox["b", "2"]]], "-", RowBox[List["4", " ", SuperscriptBox["b", "3"]]]]], ")"]]]]]], ")"]], " ", "z"]], "+", RowBox[List["10", " ", RowBox[List["(", RowBox[List["6", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["7", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "3"], "-", RowBox[List["3", " ", SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "b"]], ")"]]]], "+", RowBox[List["b", " ", RowBox[List["(", RowBox[List["28", "+", RowBox[List["3", " ", "b"]], "-", SuperscriptBox["b", "2"]]], ")"]]]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "28"]], "+", RowBox[List["3", " ", SuperscriptBox["b", "2"]]]]], ")"]]]]]], ")"]], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["10", " ", RowBox[List["(", RowBox[List["6", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["7", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["8", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "10"]], "+", SuperscriptBox["a", "2"], "-", "b", "+", SuperscriptBox["b", "2"], "-", RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "b"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["5", " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["6", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["7", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["8", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["9", "+", "a", "+", "b"]], ")"]], " ", SuperscriptBox["z", "4"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["6", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["7", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["8", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["9", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["10", "+", "a", "+", "b"]], ")"]], " ", SuperscriptBox["z", "5"]]]]], ")"]]]]]]]]








MathML Form







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<mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 110 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mn> 54 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <msup> <mi> b </mi> <mn> 4 </mn> </msup> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 49 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 54 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mn> 240 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <msup> <mi> a </mi> <mn> 5 </mn> </msup> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> 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<mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 20 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 255 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 1024 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> b </mi> <mn> 4 </mn> </msup> <mo> - </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 65 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 250 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mn> 1024 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiP </ci> <cn type='integer'> 5 </cn> <ci> a </ci> <ci> b </ci> <ci> z </ci> 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type='integer'> 10 </cn> <apply> <plus /> <ci> a </ci> <ci> b </ci> <cn type='integer'> 6 </cn> </apply> <apply> <plus /> <ci> a </ci> <ci> b </ci> <cn type='integer'> 7 </cn> </apply> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -28 </cn> </apply> <ci> a </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> b </ci> </apply> <cn type='integer'> 28 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<apply> <times /> <cn type='integer'> -4 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 110 </cn> <ci> b </ci> </apply> <cn type='integer'> 54 </cn> </apply> <ci> a </ci> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 49 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 54 </cn> <ci> b </ci> </apply> <cn type='integer'> 240 </cn> </apply> <ci> z </ci> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 5 </cn> 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type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 65 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 250 </cn> <ci> b </ci> </apply> <cn type='integer'> 1024 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29