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variants of this functions
JacobiP






Mathematica Notation

Traditional Notation









Hypergeometric Functions > JacobiP[nu,a,b,z] > Identities > Functional identities > Relations between contiguous functions > Recurrence relations





http://functions.wolfram.com/07.15.17.0003.01









  


  










Input Form





2 (\[Nu] + 1) (\[Nu] + a + b + 1) (2 \[Nu] + a + b) JacobiP[\[Nu] + 1, a, b, z] + 2 (\[Nu] + a) (\[Nu] + b) (2 \[Nu] + a + b + 2) JacobiP[\[Nu] - 1, a, b, z] == ((2 \[Nu] + a + b + 1) (a^2 - b^2) + Pochhammer[2 \[Nu] + a + b, 3] z) JacobiP[\[Nu], a, b, z]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["\[Nu]_", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Nu]_", "+", "a_", "+", "b_", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]_"]], "+", "a_", "+", "b_"]], ")"]], " ", RowBox[List["JacobiP", "[", RowBox[List[RowBox[List["\[Nu]_", "+", "1"]], ",", "a_", ",", "b_", ",", "z_"]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["\[Nu]_", "+", "a_"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Nu]_", "+", "b_"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]_"]], "+", "a_", "+", "b_", "+", "2"]], ")"]], " ", RowBox[List["JacobiP", "[", RowBox[List[RowBox[List["\[Nu]_", "-", "1"]], ",", "a_", ",", "b_", ",", "z_"]], "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "a", "+", "b", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]], ")"]]]], "+", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "a", "+", "b"]], ",", "3"]], "]"]], " ", "z"]]]], ")"]], " ", RowBox[List["JacobiP", "[", RowBox[List["\[Nu]", ",", "a", ",", "b", ",", "z"]], "]"]]]]]]]]










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





2001-10-29





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