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variants of this functions
KelvinBer






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinBer[nu,z] > Differentiation > Low-order differentiation > With respect to nu





http://functions.wolfram.com/03.18.20.0003.01









  


  










Input Form





Derivative[1, 0][KelvinBer][n, z] == ((I Pi + Log[4])/4 + Log[z] - Log[(1 + I) z]) KelvinBer[n, z] - (Pi/2) KelvinBei[n, z] - KelvinKer[n, z] + (2^(n - 1) n! Sum[(1/((n - k) k!)) (-(z/2))^k (Cos[((k - n) Pi)/4] KelvinBer[k, z] + Sin[((k - n) Pi)/4] KelvinBei[k, z]), {k, 0, n - 1}])/(-z)^n /; 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[SuperscriptBox["KelvinBer", TagBox[RowBox[List["(", RowBox[List["1", ",", "0"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "+", RowBox[List["Log", "[", "4", "]"]]]], ")"]]]], "+", RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List["Log", "[", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], "]"]]]], ")"]], " ", RowBox[List["KelvinBer", "[", RowBox[List["n", ",", "z"]], "]"]]]], "-", RowBox[List[FractionBox["1", "2"], " ", "\[Pi]", " ", RowBox[List["KelvinBei", "[", RowBox[List["n", ",", "z"]], "]"]]]], "-", RowBox[List["KelvinKer", "[", RowBox[List["n", ",", "z"]], "]"]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["n", "-", "1"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", "n"]]], " ", RowBox[List["n", "!"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["n", "-", "1"]]], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["z", "2"]]], ")"]], "k"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["k", "-", "n"]], ")"]], " ", "\[Pi]"]], "]"]], " ", RowBox[List["KelvinBer", "[", RowBox[List["k", ",", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["k", "-", "n"]], ")"]], " ", "\[Pi]"]], "]"]], " ", RowBox[List["KelvinBei", "[", RowBox[List["k", ",", "z"]], "]"]]]]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List["n", "-", "k"]], ")"]], " ", RowBox[List["k", "!"]]]]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]










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





2007-05-02