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/03.20.03.0030.01

 Input Form

 KelvinKer[8/3, z] == -(Pi z^(7/3) (45 3^(1/3) ((1 + I) z)^(4/3) ((1 - I Sqrt[3]) z^(1/3) + (1 + I) 2^(1/3) ((1 + I) z)^(1/3)) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + 90 (I 6^(1/3) z ((1 + I) z)^(2/3) + (-3)^(1/3) z^(1/3) ((1 + I) z)^(4/3)) AiryAi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + (1/2^(2/3)) (3 (40 I + 9 z^2) (2^(2/3) (I + Sqrt[3]) z^(1/3) - (2 - 2 I) ((1 + I) z)^(1/3)) AiryAiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)]) + (1/(2^(2/3) ((1 + I) z)^(2/3))) (3 z^(1/3) (-40 I + 9 z^2) (4 z^(2/3) + 2^(2/3) (-I + Sqrt[3]) ((1 + I) z)^(2/3)) AiryAiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)]) + (60 2^(1/3) 3^(5/6) z^(7/3) (z^(2/3) + (-1)^(1/6) ((-1)^(1/4) z)^(2/3)) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)])/((1 + I) z)^(4/3) + (60 2^(1/3) 3^(5/6) z^(7/3) (z^(2/3) + (-1)^(5/6) ((-1)^(1/4) z)^(2/3)) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)])/((1 + I) z)^(4/3) + (1/((1 + I) z)^(2/3)) (2 2^(1/3) Sqrt[3] z^(1/3) (40 I z^(2/3) + 9 z^(8/3) + 40 (-1)^(2/3) ((-1)^(1/4) z)^(2/3) + 9 (-1)^(1/6) z^2 ((-1)^(1/4) z)^(2/3)) AiryBiPrime[ (-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)]) - (1/((1 + I) z)^(2/3)) (2 2^(1/3) Sqrt[3] z^(1/3) (-40 I z^(2/3) + 9 z^(8/3) + 40 (-1)^(1/3) ((-1)^(1/4) z)^(2/3) + 9 (-1)^(1/3) ((-1)^(1/4) z)^(8/3)) AiryBiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)])))/(108 2^(1/3) 3^(1/6) ((-1)^(1/4) z)^(16/3))

 Standard Form

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RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]], RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "40"]], " ", "\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List["9", " ", SuperscriptBox["z", RowBox[List["8", "/", "3"]]]]], "+", RowBox[List["40", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "+", RowBox[List["9", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["8", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], ")"]]]]]], ")"]]]], ")"]]]], "/", RowBox[List["(", RowBox[List["108", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["16", "/", "3"]]]]], ")"]]]]]]]]

 MathML Form

 ker 8 3 ( z ) - π z 7 / 3 108 2 3 3 6 ( - 1 4 z ) 16 / 3 ( 60 2 3 3 5 / 6 ( z 2 / 3 + ( - 1 ) 5 / 6 ( - 1 4 z ) 2 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 7 / 3 ( ( 1 + ) z ) 4 / 3 + 60 2 3 3 5 / 6 ( z 2 / 3 + - 1 6 ( - 1 4 z ) 2 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 7 / 3 ( ( 1 + ) z ) 4 / 3 + 90 ( - 3 3 ( ( 1 + ) z ) 4 / 3 z 3 + 6 3 ( ( 1 + ) z ) 2 / 3 z ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 45 3 3 ( ( 1 + ) z ) 4 / 3 ( ( 1 - 3 ) z 3 + 2 3 ( 1 + ) ( 1 + ) z 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 3 z 3 ( 9 z 2 - 40 ) ( 4 z 2 / 3 + 2 2 / 3 ( - + 3 ) ( ( 1 + ) z ) 2 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) 2 2 / 3 ( ( 1 + ) z ) 2 / 3 + 3 ( 9 z 2 + 40 ) ( 2 2 / 3 ( + 3 ) z 3 - ( 2 - 2 ) ( 1 + ) z 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) 2 2 / 3 - 1 ( ( 1 + ) z ) 2 / 3 2 2 3 3 z 3 ( - 40 z 2 / 3 + 9 z 8 / 3 + 40 - 1 3 ( - 1 4 z ) 2 / 3 + 9 - 1 3 ( - 1 4 z ) 8 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 1 ( ( 1 + ) z ) 2 / 3 2 2 3 3 z 3 ( 40 z 2 / 3 + 9 z 8 / 3 + 9 - 1 6 ( - 1 4 z ) 2 / 3 z 2 + 40 ( - 1 ) 2 / 3 ( - 1 4 z ) 2 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) KelvinKer 8 3 z -1 z 7 3 108 2 1 3 3 1 6 -1 1 4 z 16 3 -1 60 2 1 3 3 5 6 z 2 3 -1 5 6 -1 1 4 z 2 3 AiryBi 1 2 3 2 3 1 z 2 3 z 7 3 1 z 4 3 -1 60 2 1 3 3 5 6 z 2 3 -1 1 6 -1 1 4 z 2 3 AiryBi -1 1 2 3 2 3 1 z 2 3 z 7 3 1 z 4 3 -1 90 -3 1 3 1 z 4 3 z 1 3 6 1 3 1 z 2 3 z AiryAi 1 2 3 2 3 1 z 2 3 45 3 1 3 1 z 4 3 1 -1 3 1 2 z 1 3 2 1 3 1 1 z 1 3 AiryAi -1 1 2 3 2 3 1 z 2 3 3 z 1 3 9 z 2 -1 40 4 z 2 3 2 2 3 -1 3 1 2 1 z 2 3 AiryAiPrime 1 2 3 2 3 1 z 2 3 2 2 3 1 z 2 3 -1 3 9 z 2 40 2 2 3 3 1 2 z 1 3 -1 2 -2 1 z 1 3 AiryAiPrime -1 1 2 3 2 3 1 z 2 3 2 2 3 -1 -1 1 1 z 2 3 -1 2 2 1 3 3 1 2 z 1 3 -40 z 2 3 9 z 8 3 40 -1 1 3 -1 1 4 z 2 3 9 -1 1 3 -1 1 4 z 8 3 AiryBiPrime 1 2 3 2 3 1 z 2 3 1 1 z 2 3 -1 2 2 1 3 3 1 2 z 1 3 40 z 2 3 9 z 8 3 9 -1 1 6 -1 1 4 z 2 3 z 2 40 -1 2 3 -1 1 4 z 2 3 AiryBiPrime -1 1 2 3 2 3 1 z 2 3 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKer", "[", RowBox[List[FractionBox["8", "3"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["45", " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["4", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02