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InverseJacobiCS






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.39.20.0009.01









  


  










Input Form





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










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["z_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["InverseJacobiCS", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["EllipticK", "[", FractionBox["1", RowBox[List["1", "-", "m"]]], "]"]]]], SqrtBox[RowBox[List["m", "-", "1"]]]], "-", RowBox[List["EllipticK", "[", RowBox[List["1", "-", "m"]], "]"]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["-", "\[Alpha]"]]]]], RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Alpha]"]], "]"]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["1", "-", "\[Alpha]"]]], " ", SqrtBox["\[Pi]"]]], ")"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "1"]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["3", "-", "\[Alpha]"]], "2"], ",", RowBox[List["1", "-", FractionBox["\[Alpha]", "2"]]]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["-", SuperscriptBox["z", "2"]]], ",", FractionBox[SuperscriptBox["z", "2"], RowBox[List["m", "-", "1"]]]]], "]"]]]], SqrtBox[RowBox[List["m", "-", "1"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "<", "z", "<", "1"]], "&&", RowBox[List["m", "<", "0"]]]]]]]]]]










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





2001-10-29