html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 KelvinKer

 http://functions.wolfram.com/03.20.26.0077.01

 Input Form

 Hypergeometric0F1[\[Nu] + 1, (I z^2)/4] KelvinKer[\[Nu], z] == ((1/8) Sqrt[Pi] Gamma[1 + \[Nu]] ((I MeijerG[{{}, {(5 \[Nu])/4}}, {{(2 - \[Nu])/4, -(\[Nu]/4), \[Nu]/4}, {-((3 \[Nu])/4), (5 \[Nu])/4}}, z/(2 Sqrt[2]), 1/4] + MeijerG[{{}, {(2 + 5 \[Nu])/4}}, {{(2 - \[Nu])/4, -(\[Nu]/4), \[Nu]/4}, {-((3 \[Nu])/4), (2 + 5 \[Nu])/4}}, z/(2 Sqrt[2]), 1/4])/ 2^(\[Nu]/2) + (1/(Sqrt[2] Pi)) ((-I) MeijerG[{{(1 - \[Nu])/4, (3 - \[Nu])/4}, {}}, {{(2 - \[Nu])/4, \[Nu]/4, (2 + \[Nu])/4}, {(2 - 3 \[Nu])/4, -((3 \[Nu])/4), -(\[Nu]/4)}}, z/2, 1/4] + MeijerG[{{(1 - \[Nu])/4, (3 - \[Nu])/4}, {}}, {{-(\[Nu]/4), \[Nu]/4, (2 + \[Nu])/4}, {(2 - 3 \[Nu])/4, (2 - \[Nu])/4, -((3 \[Nu])/4)}}, z/2, 1/4])))/E^((3/4) I Pi \[Nu])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Hypergeometric0F1", "[", RowBox[List[RowBox[List["\[Nu]", "+", "1"]], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]], "4"]]], "]"]], RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "\[Equal]", " ", RowBox[List[FractionBox["1", "8"], SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["3", "4"]]], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Nu]"]], "]"]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "\[Nu]"]], "/", "2"]]], RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", FractionBox[RowBox[List["5", " ", "\[Nu]"]], "4"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["2", "-", "\[Nu]"]], "4"], ",", RowBox[List["-", FractionBox["\[Nu]", "4"]]], ",", FractionBox["\[Nu]", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["3", " ", "\[Nu]"]], "4"]]], ",", FractionBox[RowBox[List["5", " ", "\[Nu]"]], "4"]]], "}"]]]], "}"]], ",", FractionBox["z", RowBox[List["2", " ", SqrtBox["2"]]]], ",", FractionBox["1", "4"]]], "]"]]]], "+", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", FractionBox[RowBox[List["2", "+", RowBox[List["5", " ", "\[Nu]"]]]], "4"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["2", "-", "\[Nu]"]], "4"], ",", RowBox[List["-", FractionBox["\[Nu]", "4"]]], ",", FractionBox["\[Nu]", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["3", " ", "\[Nu]"]], "4"]]], ",", FractionBox[RowBox[List["2", "+", RowBox[List["5", " ", "\[Nu]"]]]], "4"]]], "}"]]]], "}"]], ",", FractionBox["z", RowBox[List["2", " ", SqrtBox["2"]]]], ",", FractionBox["1", "4"]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List[SqrtBox["2"], " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "4"], ",", FractionBox[RowBox[List["3", "-", "\[Nu]"]], "4"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["2", "-", "\[Nu]"]], "4"], ",", FractionBox["\[Nu]", "4"], ",", FractionBox[RowBox[List["2", "+", "\[Nu]"]], "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["2", "-", RowBox[List["3", " ", "\[Nu]"]]]], "4"], ",", RowBox[List["-", FractionBox[RowBox[List["3", " ", "\[Nu]"]], "4"]]], ",", RowBox[List["-", FractionBox["\[Nu]", "4"]]]]], "}"]]]], "}"]], ",", FractionBox["z", "2"], ",", FractionBox["1", "4"]]], "]"]]]], "+", " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "4"], ",", FractionBox[RowBox[List["3", "-", "\[Nu]"]], "4"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "4"]]], ",", FractionBox["\[Nu]", "4"], ",", FractionBox[RowBox[List["2", "+", "\[Nu]"]], "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["2", "-", RowBox[List["3", " ", "\[Nu]"]]]], "4"], ",", FractionBox[RowBox[List["2", "-", "\[Nu]"]], "4"], ",", RowBox[List["-", FractionBox[RowBox[List["3", " ", "\[Nu]"]], "4"]]]]], "}"]]]], "}"]], ",", FractionBox["z", "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] ker ν ( z ) 1 8 - 3 π ν 4 π Γ ( ν + 1 ) ( 2 - ν 2 ( G 1 , 5 3 , 0 ( z 2 2 , 1 4 5 ν 4 2 - ν 4 , - ν 4 , ν 4 , - 1 4 ( 3 ν ) , 5 ν 4 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["1", ",", "5"]], RowBox[List["3", ",", "0"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[FractionBox["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[TagBox[FractionBox[RowBox[List["5", " ", "\[Nu]"]], "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]], List[RowBox[List[TagBox[FractionBox[RowBox[List["2", "-", "\[Nu]"]], "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["\[Nu]", "4"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["\[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]], ",", TagBox[FractionBox[RowBox[List["5", " ", "\[Nu]"]], "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] + G 1 , 5 3 , 0 ( z 2 2 , 1 4 1 4 ( 5 ν + 2 ) 2 - ν 4 , - ν 4 , ν 4 , - 1 4 ( 3 ν ) , 1 4 ( 5 ν + 2 ) ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["1", ",", "5"]], RowBox[List["3", ",", "0"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[FractionBox["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[TagBox[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", "\[Nu]"]], "+", "2"]], ")"]]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]], List[RowBox[List[TagBox[FractionBox[RowBox[List["2", "-", "\[Nu]"]], "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["\[Nu]", "4"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["\[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]], ",", TagBox[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", "\[Nu]"]], "+", "2"]], ")"]]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] ) + 1 2 π ( G 2 , 6 3 , 2 ( z 2 , 1 4 1 - ν 4 , 3 - ν 4 - ν 4 , ν 4 , ν + 2 4 , 1 4 ( 2 - 3 ν ) , 2 - ν 4 , - 1 4 ( 3 ν ) ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "6"]], RowBox[List["3", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[FractionBox["z", "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[RowBox[List["1", "-", "\[Nu]"]], "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox[RowBox[List["3", "-", "\[Nu]"]], "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox[RowBox[List["-", FractionBox["\[Nu]", "4"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["\[Nu]", "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox[RowBox[List["\[Nu]", "+", "2"]], "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["3", " ", "\[Nu]"]]]], ")"]]]], 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]] - G 2 , 6 3 , 2 ( z 2 , 1 4 1 - ν 4 , 3 - ν 4 2 - ν 4 , ν 4 , ν + 2 4 , 1 4 ( 2 - 3 ν ) , - 1 4 ( 3 ν ) , - ν 4 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "6"]], RowBox[List["3", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[FractionBox["z", "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[RowBox[List["1", "-", "\[Nu]"]], "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox[RowBox[List["3", "-", "\[Nu]"]], "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox[FractionBox[RowBox[List["2", "-", "\[Nu]"]], "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["\[Nu]", "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox[RowBox[List["\[Nu]", "+", "2"]], "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["3", " ", "\[Nu]"]]]], ")"]]]], 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]], ",", TagBox[RowBox[List["-", FractionBox["\[Nu]", "4"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] ) ) Hypergeometric0F1 ν 1 z 2 4 -1 KelvinKer ν z 1 8 -1 3 ν 4 -1 1 2 Gamma ν 1 2 -1 ν 2 -1 MeijerG 5 ν 4 -1 2 -1 ν 4 -1 -1 ν 4 -1 ν 4 -1 -1 1 4 3 ν 5 ν 4 -1 z 2 2 1 2 -1 1 4 MeijerG 1 4 5 ν 2 2 -1 ν 4 -1 -1 ν 4 -1 ν 4 -1 -1 1 4 3 ν 1 4 5 ν 2 z 2 2 1 2 -1 1 4 1 2 1 2 -1 MeijerG 1 -1 ν 4 -1 3 -1 ν 4 -1 -1 ν 4 -1 ν 4 -1 ν 2 4 -1 1 4 2 -1 3 ν 2 -1 ν 4 -1 -1 1 4 3 ν z 2 -1 1 4 -1 MeijerG 1 -1 ν 4 -1 3 -1 ν 4 -1 2 -1 ν 4 -1 ν 4 -1 ν 2 4 -1 1 4 2 -1 3 ν -1 1 4 3 ν -1 ν 4 -1 z 2 -1 1 4 [/itex]

 Rule Form

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

 2007-05-02