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/03.20.03.0027.01

 Input Form

 KelvinKer[5/3, z] == (Pi (6 (-2)^(1/3) 3^(5/6) (-3 I + Sqrt[3]) z^3 ((1 + I) z)^(4/3) ((-(-2)^(2/3)) z^(1/3) + (1 + I) ((1 + I) z)^(1/3)) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] - 72 3^(1/3) ((1 + I) z)^(4/3) ((-1)^(5/6) z^(10/3) + ((-1)^(1/4) z)^(10/3)) AiryAi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + 192 (-1)^(2/3) z^3 (z^(1/3) + (-1)^(7/12) ((-1)^(1/4) z)^(1/3)) AiryAiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + 192 ((-1)^(5/6) z^(10/3) + ((-1)^(1/4) z)^(10/3)) AiryAiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + 6 (-2)^(1/3) 3^(5/6) ((1 + I) z)^(4/3) (-2 (-1)^(1/3) 2^(2/3) z^(10/3) + (-1)^(1/6) ((1 + I) z)^(10/3)) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] - 24 3^(5/6) ((1 + I) z)^(4/3) ((-1)^(5/6) z^(10/3) - ((-1)^(1/4) z)^(10/3)) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] - 64 (-1)^(2/3) Sqrt[3] z (-z^(7/3) + (-1)^(1/3) z ((-1)^(1/4) z)^(4/3)) AiryBiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + 64 Sqrt[3] ((-1)^(5/6) z^(10/3) - ((-1)^(1/4) z)^(10/3)) AiryBiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)]))/ (288 2^(1/3) 3^(1/6) z^(2/3) ((-1)^(1/4) z)^(13/3))

 Standard Form

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RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], "+", RowBox[List["64", " ", SqrtBox["3"], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["10", "/", "3"]]]]], "-", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["10", "/", "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["288", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["13", "/", "3"]]]]], ")"]]]]]]]]

 MathML Form

 ker 5 3 ( z ) π 288 2 3 3 6 z 2 / 3 ( - 1 4 z ) 13 / 3 ( - 72 3 3 ( ( - 1 ) 5 / 6 z 10 / 3 + ( - 1 4 z ) 10 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 4 / 3 + 6 - 2 3 3 5 / 6 ( - 3 + 3 ) z 3 ( ( 1 + ) ( 1 + ) z 3 - ( - 2 ) 2 / 3 z 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 4 / 3 - 24 3 5 / 6 ( ( - 1 ) 5 / 6 z 10 / 3 - ( - 1 4 z ) 10 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 4 / 3 + 6 - 2 3 3 5 / 6 ( - 1 6 ( ( 1 + ) z ) 10 / 3 - 2 - 1 3 2 2 / 3 z 10 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 4 / 3 + 192 ( ( - 1 ) 5 / 6 z 10 / 3 + ( - 1 4 z ) 10 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 192 ( - 1 ) 2 / 3 z 3 ( z 3 + ( - 1 ) 7 / 12 - 1 4 z 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 64 3 ( ( - 1 ) 5 / 6 z 10 / 3 - ( - 1 4 z ) 10 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) - 64 ( - 1 ) 2 / 3 3 z ( - 1 3 z ( - 1 4 z ) 4 / 3 - z 7 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) KelvinKer 5 3 z 288 2 1 3 3 1 6 z 2 3 -1 1 4 z 13 3 -1 -72 3 1 3 -1 5 6 z 10 3 -1 1 4 z 10 3 AiryAi 1 2 3 2 3 1 z 2 3 1 z 4 3 6 -2 1 3 3 5 6 -3 3 1 2 z 3 1 1 z 1 3 -1 -2 2 3 z 1 3 AiryAi -1 1 2 3 2 3 1 z 2 3 1 z 4 3 -1 24 3 5 6 -1 5 6 z 10 3 -1 -1 1 4 z 10 3 AiryBi 1 2 3 2 3 1 z 2 3 1 z 4 3 6 -2 1 3 3 5 6 -1 1 6 1 z 10 3 -1 2 -1 1 3 2 2 3 z 10 3 AiryBi -1 1 2 3 2 3 1 z 2 3 1 z 4 3 192 -1 5 6 z 10 3 -1 1 4 z 10 3 AiryAiPrime 1 2 3 2 3 1 z 2 3 192 -1 2 3 z 3 z 1 3 -1 7 12 -1 1 4 z 1 3 AiryAiPrime -1 1 2 3 2 3 1 z 2 3 64 3 1 2 -1 5 6 z 10 3 -1 -1 1 4 z 10 3 AiryBiPrime 1 2 3 2 3 1 z 2 3 -1 64 -1 2 3 3 1 2 z -1 1 3 z -1 1 4 z 4 3 -1 z 7 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["5", "3"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["6", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "2"]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["5", "/", "6"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", "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["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "2"]], ")"]], RowBox[List["2", "/", "3"]]]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02