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InverseJacobiCS






Mathematica Notation

Traditional Notation









Elliptic Functions > InverseJacobiCS[z,m] > Differentiation > Fractional integro-differentiation > With respect to m





http://functions.wolfram.com/09.39.20.0010.01









  


  










Input Form





D[InverseJacobiCS[z, m], {m, \[Alpha]}] == (Sqrt[Pi]/(m^\[Alpha] (2 Sqrt[z^2 + 1]))) HypergeometricPFQRegularized[ {{1/2}, {1/2}, {1/2, 1}}, {{3/2}, {}, {1 - \[Alpha]}}, 1/(z^2 + 1), m/(z^2 + 1)] /; z > 0 && m < 1










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["m_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["InverseJacobiCS", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["m", RowBox[List["-", "\[Alpha]"]]], " ", SqrtBox["\[Pi]"]]], ")"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "1"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["3", "2"], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["1", "-", "\[Alpha]"]], "}"]]]], "}"]], ",", FractionBox["1", RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]], ",", FractionBox["m", RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]]]], "]"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]]]]], "/;", RowBox[List[RowBox[List["z", ">", "0"]], "&&", RowBox[List["m", "<", "1"]]]]]]]]]]










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





2001-10-29