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variants of this functions
JacobiP




Mathematica Notation

Traditional Notation









Hypergeometric Functions > JacobiP[nu,a,b,z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving power function





http://functions.wolfram.com/07.15.21.0002.01









  


  








Input Form





Integrate[z^(\[Alpha] - 1) JacobiP[\[Nu], a, b, z], z] == ((Pochhammer[a + 1, \[Nu]] z^\[Alpha])/(\[Alpha] Gamma[\[Nu] + 1])) HypergeometricPFQRegularized[{{-\[Nu], a + b + \[Nu] + 1}, {\[Alpha]}, {}}, {{a + 1}, {\[Alpha] + 1}, {}}, -(z/2), 1/2]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", RowBox[List["\[Alpha]_", "-", "1"]]], " ", RowBox[List["JacobiP", "[", RowBox[List["\[Nu]_", ",", "a_", ",", "b_", ",", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["a", "+", "1"]], ",", "\[Nu]"]], "]"]], " ", SuperscriptBox["z", "\[Alpha]"]]], ")"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", RowBox[List["a", "+", "b", "+", "\[Nu]", "+", "1"]]]], "}"]], ",", RowBox[List["{", "\[Alpha]", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["a", "+", "1"]], "}"]], ",", RowBox[List["{", RowBox[List["\[Alpha]", "+", "1"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["-", FractionBox["z", "2"]]], ",", FractionBox["1", "2"]]], "]"]]]], RowBox[List["\[Alpha]", " ", RowBox[List["Gamma", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]]]]]]]]]


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





2001-10-29