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 JacobiP

 http://functions.wolfram.com/05.06.17.0008.01

 Input Form

 JacobiP[n, a, b, z] - JacobiP[n, a - 1, b, z] == ((z + 1)/2) JacobiP[n - 1, a, b + 1, z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["JacobiP", "[", RowBox[List["n", ",", "a", ",", "b", ",", "z"]], "]"]], "-", RowBox[List["JacobiP", "[", RowBox[List["n", ",", RowBox[List["a", "-", "1"]], ",", "b", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["z", "+", "1"]], "2"], RowBox[List["JacobiP", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", "a", ",", RowBox[List["b", "+", "1"]], ",", "z"]], "]"]]]]]]]]

 MathML Form

 P n ( a , b ) ( z ) - P n ( a - 1 , b ) ( z ) z + 1 2 P n - 1 ( a , b + 1 ) ( z ) JacobiP n a b z -1 JacobiP n a -1 b z z 1 2 -1 JacobiP n -1 a b 1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["JacobiP", "[", RowBox[List["n_", ",", "a_", ",", "b_", ",", "z_"]], "]"]], "-", RowBox[List["JacobiP", "[", RowBox[List["n_", ",", RowBox[List["a_", "-", "1"]], ",", "b_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], " ", RowBox[List["JacobiP", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", "a", ",", RowBox[List["b", "+", "1"]], ",", "z"]], "]"]]]]]]]]

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

 2001-10-29