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/03.20.03.0009.01

 Input Form

 KelvinKer[-(8/3), z] == ((1 - I)/(216 6^(1/6) z^(11/3))) (-1)^(3/4) Pi ((-45 - 45 I) 3^(1/3) z^2 ((-2 - 2 I) z^(1/3) + 2^(1/3) (-I + Sqrt[3]) ((1 + I) z)^(1/3)) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (45 + 45 I) 3^(1/3) z^2 ((2 + 2 I) z^(1/3) + 2^(1/3) (I + Sqrt[3]) ((1 + I) z)^(1/3)) AiryAi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + 6 I z^(1/3) (40 I + 9 z^2) (I (-2)^(1/3) z^(2/3) + ((1 + I) z)^(2/3)) AiryAiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] - 6 (40 (-1)^(1/6) 2^(1/3) z + 9 (-1)^(2/3) 2^(1/3) z^3 + 40 z^(1/3) ((1 + I) z)^(2/3) + 9 I z^(7/3) ((1 + I) z)^(2/3)) AiryAiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + (30 - 30 I) 3^(5/6) z^2 ((-1 + I) z^(1/3) + (-2)^(1/3) ((1 + I) z)^(1/3)) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] - (15 + 15 I) 3^(1/3) z^2 ((-2 - 2 I) Sqrt[3] z^(1/3) + 2^(1/3) (3 + I Sqrt[3]) ((1 + I) z)^(1/3)) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + 2 Sqrt[3] z^(1/3) (40 I + 9 z^2) ((-2)^(1/3) z^(2/3) + I ((1 + I) z)^(2/3)) AiryBiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + 2 Sqrt[3] z^(1/3) (40 (-1)^(1/6) 2^(1/3) z^(2/3) + 9 (-1)^(2/3) 2^(1/3) z^(8/3) - 40 ((1 + I) z)^(2/3) - 9 I z^2 ((1 + I) z)^(2/3)) AiryBiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)])

 Standard Form

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SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "6"]]], " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List["9", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["8", "/", "3"]]]]], "-", RowBox[List["40", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "-", RowBox[List["9", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "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"]]]]], "]"]]]]]], ")"]]]]]]]]

 MathML Form

 ker - 8 3 ( z ) ( 1 - ) ( - 1 ) 3 / 4 π 216 6 6 z 11 / 3 ( 6 ( 9 z 2 + 40 ) ( - 2 3 z 2 / 3 + ( ( 1 + ) z ) 2 / 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 + 2 3 ( 40 - 1 6 2 3 z 2 / 3 + 9 ( - 1 ) 2 / 3 2 3 z 8 / 3 - 9 ( ( 1 + ) z ) 2 / 3 z 2 - 40 ( ( 1 + ) z ) 2 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 + 2 3 ( 9 z 2 + 40 ) ( - 2 3 z 2 / 3 + ( ( 1 + ) z ) 2 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 + 3 3 ( 45 + 45 ) ( ( 2 + 2 ) z 3 + 2 3 ( + 3 ) ( 1 + ) z 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 + 3 3 ( - 45 - 45 ) ( ( - 2 - 2 ) z 3 + 2 3 ( - + 3 ) ( 1 + ) z 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 - ( 15 + 15 ) 3 3 ( 3 ( - 2 - 2 ) z 3 + 2 3 ( 3 + 3 ) ( 1 + ) z 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 + 3 5 / 6 ( 30 - 30 ) ( ( - 1 + ) z 3 + - 2 3 ( 1 + ) z 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 - 6 ( 40 ( ( 1 + ) z ) 2 / 3 z 3 + 9 ( ( 1 + ) z ) 2 / 3 z 7 / 3 + 9 ( - 1 ) 2 / 3 2 3 z 3 + 40 - 1 6 2 3 z ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) KelvinKer -1 8 3 z 1 -1 -1 3 4 216 6 1 6 z 11 3 -1 6 9 z 2 40 -2 1 3 z 2 3 1 z 2 3 AiryAiPrime -1 1 2 3 2 3 1 z 2 3 z 1 3 2 3 1 2 40 -1 1 6 2 1 3 z 2 3 9 -1 2 3 2 1 3 z 8 3 -1 9 1 z 2 3 z 2 -1 40 1 z 2 3 AiryBiPrime 1 2 3 2 3 1 z 2 3 z 1 3 2 3 1 2 9 z 2 40 -2 1 3 z 2 3 1 z 2 3 AiryBiPrime -1 1 2 3 2 3 1 z 2 3 z 1 3 3 1 3 45 45 2 2 z 1 3 2 1 3 3 1 2 1 z 1 3 AiryAi 1 2 3 2 3 1 z 2 3 z 2 3 1 3 -45 -45 -2 -2 z 1 3 2 1 3 -1 3 1 2 1 z 1 3 AiryAi -1 1 2 3 2 3 1 z 2 3 z 2 -1 15 15 3 1 3 3 1 2 -2 -2 z 1 3 2 1 3 3 3 1 2 1 z 1 3 AiryBi 1 2 3 2 3 1 z 2 3 z 2 3 5 6 30 -30 -1 z 1 3 -2 1 3 1 z 1 3 AiryBi -1 1 2 3 2 3 1 z 2 3 z 2 -1 6 40 1 z 2 3 z 1 3 9 1 z 2 3 z 7 3 9 -1 2 3 2 1 3 z 3 40 -1 1 6 2 1 3 z AiryAiPrime 1 2 3 2 3 1 z 2 3 [/itex]

 Rule Form

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

 2007-05-02