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/03.20.03.0006.01

 Input Form

 KelvinKer[-(11/3), z] == (1/(324 2^(5/6) 3^(1/6) z^(14/3))) (I Pi (9 3^(1/3) z^2 (160 I + 9 z^2) ((1 - I) 2^(2/3) z^(1/3) + (1 + I Sqrt[3]) ((1 + I) z)^(1/3)) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] - 9 I 3^(1/3) z^2 (-160 I + 9 z^2) ((1 - I) 2^(2/3) z^(1/3) + (1 - I Sqrt[3]) ((1 + I) z)^(1/3)) AiryAi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + (60 + 60 I) (-64 (-1)^(1/3) z + 18 (-1)^(5/6) z^3 + 32 I 2^(2/3) z^(1/3) ((1 + I) z)^(2/3) + 9 2^(2/3) z^(7/3) ((1 + I) z)^(2/3)) AiryAiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] - (60 + 60 I) (64 (-1)^(1/6) z + 18 (-1)^(2/3) z^3 + 32 2^(2/3) z^(1/3) ((1 + I) z)^(2/3) + 9 I 2^(2/3) z^(7/3) ((1 + I) z)^(2/3)) AiryAiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] - 3 3^(1/3) z^2 (160 I + 9 z^2) ((-1 + I) 2^(2/3) Sqrt[3] z^(1/3) + (3 I + Sqrt[3]) ((1 + I) z)^(1/3)) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + 3 I 3^(1/3) z^2 (160 + 9 I z^2) ((1 + I) 2^(2/3) Sqrt[3] z^(1/3) + (-3 - I Sqrt[3]) ((1 + I) z)^(1/3)) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + (20 + 20 I) Sqrt[3] z^(1/3) (64 (-1)^(1/3) z^(2/3) - 18 (-1)^(5/6) z^(8/3) + 32 I 2^(2/3) ((1 + I) z)^(2/3) + 9 2^(2/3) z^2 ((1 + I) z)^(2/3)) AiryBiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (20 + 20 I) Sqrt[3] z^(1/3) (64 (-1)^(1/6) z^(2/3) + 18 (-1)^(2/3) z^(8/3) - 32 2^(2/3) ((1 + I) z)^(2/3) - 9 I 2^(2/3) z^2 ((1 + I) z)^(2/3)) AiryBiPrime[ (1/2) 3^(2/3) ((1 + I) z)^(2/3)]))

 Standard Form

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RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryAi", "[", 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["9", " ", "\[ImaginaryI]", " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "160"]], " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox["2", RowBox[List["2", "/", 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"3"]]]]], "-", RowBox[List["18", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["8", "/", "3"]]]]], "+", RowBox[List["32", " ", "\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "+", RowBox[List["9", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "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[RowBox[List["(", RowBox[List["20", "+", RowBox[List["20", " ", "\[ImaginaryI]"]]]], ")"]], " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["64", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List["18", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["8", "/", "3"]]]]], "-", RowBox[List["32", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "-", RowBox[List["9", " ", "\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", 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 - 11 3 ( z ) π 324 2 5 / 6 3 6 z 14 / 3 ( 3 ( 20 + 20 ) ( 64 - 1 6 z 2 / 3 + 18 ( - 1 ) 2 / 3 z 8 / 3 - 9 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 2 - 32 2 2 / 3 ( ( 1 + ) z ) 2 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 + 3 ( 20 + 20 ) ( 64 - 1 3 z 2 / 3 - 18 ( - 1 ) 5 / 6 z 8 / 3 + 9 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 2 + 32 2 2 / 3 ( ( 1 + ) z ) 2 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 - 9 3 3 ( 9 z 2 - 160 ) ( 2 2 / 3 ( 1 - ) z 3 + ( 1 - 3 ) ( 1 + ) z 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 + 9 3 3 ( 9 z 2 + 160 ) ( 2 2 / 3 ( 1 - ) z 3 + ( 1 + 3 ) ( 1 + ) z 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 + 3 3 3 ( 9 z 2 + 160 ) ( 2 2 / 3 3 ( 1 + ) z 3 + ( - 3 - 3 ) ( 1 + ) z 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 - 3 3 3 ( 9 z 2 + 160 ) ( 2 2 / 3 3 ( - 1 + ) z 3 + ( 3 + 3 ) ( 1 + ) z 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 - ( 60 + 60 ) ( 32 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 3 + 9 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 7 / 3 + 18 ( - 1 ) 2 / 3 z 3 + 64 - 1 6 z ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + ( 60 + 60 ) ( 32 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 3 + 9 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 7 / 3 + 18 ( - 1 ) 5 / 6 z 3 - 64 - 1 3 z ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) KelvinKer -1 11 3 z 324 2 5 6 3 1 6 z 14 3 -1 3 1 2 20 20 64 -1 1 6 z 2 3 18 -1 2 3 z 8 3 -1 9 2 2 3 1 z 2 3 z 2 -1 32 2 2 3 1 z 2 3 AiryBiPrime 1 2 3 2 3 1 z 2 3 z 1 3 3 1 2 20 20 64 -1 1 3 z 2 3 -1 18 -1 5 6 z 8 3 9 2 2 3 1 z 2 3 z 2 32 2 2 3 1 z 2 3 AiryBiPrime -1 1 2 3 2 3 1 z 2 3 z 1 3 -1 9 3 1 3 9 z 2 -1 160 2 2 3 1 -1 z 1 3 1 -1 3 1 2 1 z 1 3 AiryAi 1 2 3 2 3 1 z 2 3 z 2 9 3 1 3 9 z 2 160 2 2 3 1 -1 z 1 3 1 3 1 2 1 z 1 3 AiryAi -1 1 2 3 2 3 1 z 2 3 z 2 3 3 1 3 9 z 2 160 2 2 3 3 1 2 1 z 1 3 -3 -1 3 1 2 1 z 1 3 AiryBi 1 2 3 2 3 1 z 2 3 z 2 -1 3 3 1 3 9 z 2 160 2 2 3 3 1 2 -1 z 1 3 3 3 1 2 1 z 1 3 AiryBi -1 1 2 3 2 3 1 z 2 3 z 2 -1 60 60 32 2 2 3 1 z 2 3 z 1 3 9 2 2 3 1 z 2 3 z 7 3 18 -1 2 3 z 3 64 -1 1 6 z AiryAiPrime 1 2 3 2 3 1 z 2 3 60 60 32 2 2 3 1 z 2 3 z 1 3 9 2 2 3 1 z 2 3 z 7 3 18 -1 5 6 z 3 -1 64 -1 1 3 z AiryAiPrime -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[RowBox[List["-", FractionBox["11", "3"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["9", " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["160", " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02