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 KelvinBei

 http://functions.wolfram.com/03.17.26.0086.01

 Input Form

 Hypergeometric0F1[1 + \[Nu], (I z^2)/4] KelvinBei[\[Nu], z] == ((-I) 2^(-1 - \[Nu]/2) Sqrt[Pi] z^\[Nu] Gamma[1 + \[Nu]] (E^((3 I Pi \[Nu])/2) 2^(3 (\[Nu]/2)) Csc[Pi (3/4 + \[Nu])] MeijerG[{{(1 - \[Nu])/2}, {(1 - 2 \[Nu])/4}}, {{\[Nu]/2}, {-(\[Nu]/2), -((3 \[Nu])/2), (1 - 2 \[Nu])/4}}, (-1)^(1/4) z, 1/2] - MeijerG[{{}, {}}, {{\[Nu]/4}, {-(\[Nu]/4), (2 - \[Nu])/4, -((3 \[Nu])/4)}}, ((-1)^(1/4) z)/(2 Sqrt[2]), 1/4]))/(E^((3/4) I Pi \[Nu]) ((-1)^(1/4) z)^\[Nu])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Hypergeometric0F1", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]], "4"]]], "]"]], RowBox[List["KelvinBei", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", FractionBox["\[Nu]", "2"]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["3", "4"]]], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]]], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", "\[Nu]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Nu]"]], "]"]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]], SuperscriptBox["2", RowBox[List["3", RowBox[List["\[Nu]", "/", "2"]]]]], " ", RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[FractionBox["3", "4"], "+", "\[Nu]"]], ")"]]]], "]"]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], "}"]], ",", RowBox[List["{", FractionBox[RowBox[List["1", "-", RowBox[List["2", " ", "\[Nu]"]]]], "4"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["\[Nu]", "2"], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["-", FractionBox[RowBox[List["3", " ", "\[Nu]"]], "2"]]], ",", FractionBox[RowBox[List["1", "-", RowBox[List["2", " ", "\[Nu]"]]]], "4"]]], "}"]]]], "}"]], ",", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ",", FractionBox["1", "2"]]], "]"]]]], "-", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["\[Nu]", "4"], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "4"]]], ",", FractionBox[RowBox[List["2", "-", "\[Nu]"]], "4"], ",", RowBox[List["-", FractionBox[RowBox[List["3", "\[Nu]"]], "4"]]]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], RowBox[List["2", SqrtBox["2"]]]], ",", FractionBox["1", "4"]]], "]"]]]], ")"]]]]]]]]

 MathML Form

 0 F 1 ( ; ν + 1 ; z 2 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "0"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["\[Nu]", "+", "1"]], Hypergeometric0F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]], "4"], Hypergeometric0F1, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], Hypergeometric0F1] bei ν ( z ) - 2 - ν 2 - 1 1 4 ( - 3 ) π ν π z ν ( - 1 4 z ) - ν Γ ( ν + 1 ) ( 3 π ν 2 2 3 ν 2 csc ( π ( ν + 3 4 ) ) G 2 , 4 1 , 1 ( - 1 4 z , 1 2 1 - ν 2 , 1 4 ( 1 - 2 ν ) ν 2 , - ν 2 , - 1 2 ( 3 ν ) , 1 4 ( 1 - 2 ν ) ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "4"]], RowBox[List["1", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[RowBox[List[RadicalBox[RowBox[List["-", "1"]], "4"], " ", "z"]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]], MeijerG], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox[FractionBox["\[Nu]", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["\[Nu]", "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["3", " ", "\[Nu]"]], ")"]]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] - G 0 , 4 1 , 0 ( - 1 4 z 2 2 , 1 4 ν 4 , - ν 4 , 2 - ν 4 , - 1 4 ( 3 ν ) ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["0", ",", "4"]], RowBox[List["1", ",", "0"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RadicalBox[RowBox[List["-", "1"]], "4"], " ", "z"]], RowBox[List["2", " ", SqrtBox["2"]]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]], MeijerG], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[FractionBox["\[Nu]", "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["\[Nu]", "4"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox[RowBox[List["2", "-", "\[Nu]"]], "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List["(", RowBox[List["3", " ", "\[Nu]"]], ")"]]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] ) Hypergeometric0F1 ν 1 z 2 4 -1 KelvinBei ν z -1 2 -1 ν 2 -1 -1 1 4 -3 ν 1 2 z ν -1 1 4 z -1 ν Gamma ν 1 3 ν 2 -1 2 3 ν 2 -1 ν 3 4 MeijerG 1 -1 ν 2 -1 1 4 1 -1 2 ν ν 2 -1 -1 ν 2 -1 -1 1 2 3 ν 1 4 1 -1 2 ν -1 1 4 z 1 2 -1 MeijerG ν 4 -1 -1 ν 4 -1 2 -1 ν 4 -1 -1 1 4 3 ν -1 1 4 z 2 2 1 2 -1 1 4 [/itex]

 Rule Form

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

 2007-05-02