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BesselI




Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselI[nu,z] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/03.02.20.0017.01









  


  








Input Form





D[BesselI[-n, z], {z, \[Alpha]}] == 2^(\[Alpha] - 2 n) Sqrt[Pi] z^(-\[Alpha] + n) Gamma[1 + n] HypergeometricPFQRegularized[ {(1 + n)/2, (2 + n)/2}, {(1/2) (1 - \[Alpha] + n), (1/2) (2 - \[Alpha] + n), 1 + n}, z^2/4] /; Element[n, Integers] && n > 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["BesselI", "[", RowBox[List[RowBox[List["-", "n_"]], ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["\[Alpha]", "-", RowBox[List["2", " ", "n"]]]]], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "\[Alpha]"]], "+", "n"]]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "n"]], "]"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "+", "n"]], "2"], ",", FractionBox[RowBox[List["2", "+", "n"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", "\[Alpha]", "+", "n"]], ")"]]]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "-", "\[Alpha]", "+", "n"]], ")"]]]], ",", RowBox[List["1", "+", "n"]]]], "}"]], ",", FractionBox[SuperscriptBox["z", "2"], "4"]]], "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]


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





2001-10-29