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/03.20.03.0033.01

 Input Form

 KelvinKer[11/3, z] == ((I - 1)/(648 2^(5/6) 3^(1/6) z^(13/3))) Pi (-9 3^(1/3) z^(5/3) (160 I + 9 z^2) (2^(2/3) (I + Sqrt[3]) z^(1/3) - (2 - 2 I) ((1 + I) z)^(1/3)) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (1/((1 + I) z)^(8/3)) (18 3^(1/3) z^4 (-160 I + 9 z^2) (4 z^(2/3) + 2^(2/3) (-I + Sqrt[3]) ((1 + I) z)^(2/3)) AiryAi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)]) + (1/((1 + I) z)^(4/3)) (120 I z^(5/3) (32 I + 9 z^2) (2^(2/3) (1 - 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)]) + 60 (-32 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)] + 3 I 3^(1/3) z^(5/3) (160 I + 9 z^2) ((-2^(2/3)) (-3 I + Sqrt[3]) z^(1/3) + (2 + 2 I) Sqrt[3] ((1 + I) z)^(1/3)) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + 3 3^(1/3) z^(5/3) (-160 I + 9 z^2) ((-2^(2/3)) (3 I + Sqrt[3]) z^(1/3) + (2 + 2 I) Sqrt[3] ((1 + I) z)^(1/3)) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] - 20 I (32 I + 9 z^2) (4 Sqrt[3] z^(2/3) + 2^(2/3) (3 + I Sqrt[3]) ((1 + I) z)^(2/3)) AiryBiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] - 20 I (-32 I + 9 z^2) (-4 I Sqrt[3] z^(2/3) + 2^(2/3) (3 I + Sqrt[3]) ((1 + I) z)^(2/3)) AiryBiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["KelvinKer", "[", RowBox[List[FractionBox["11", "3"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", "-", "1"]], RowBox[List["648", " ", SuperscriptBox["2", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["13", "/", "3"]]]]]], "\[Pi]", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "9"]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["5", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["160", " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["2", "-", 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RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryBi", "[", 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["20", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["32", " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", 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["20", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "32"]], " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "\[ImaginaryI]", " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", 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 ) ( - 1 ) π 648 2 5 / 6 3 6 z 13 / 3 ( - 9 3 3 ( 9 z 2 + 160 ) ( 2 2 / 3 ( + 3 ) z 3 - ( 2 - 2 ) ( 1 + ) z 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 5 / 3 + 3 3 3 ( 9 z 2 - 160 ) ( ( 2 + 2 ) 3 ( 1 + ) z 3 - 2 2 / 3 ( 3 + 3 ) z 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 5 / 3 + 3 3 3 ( 9 z 2 + 160 ) ( ( 2 + 2 ) 3 ( 1 + ) z 3 - 2 2 / 3 ( - 3 + 3 ) z 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 5 / 3 + 18 3 3 z 4 ( 9 z 2 - 160 ) ( 4 z 2 / 3 + 2 2 / 3 ( - + 3 ) ( ( 1 + ) z ) 2 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 8 / 3 + 60 ( 9 z 2 - 32 ) ( 4 z 2 / 3 + 2 2 / 3 ( - + 3 ) ( ( 1 + ) z ) 2 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 120 z 5 / 3 ( 9 z 2 + 32 ) ( 2 2 / 3 ( 1 - 3 ) z 3 + ( 2 + 2 ) ( 1 + ) z 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 4 / 3 - 20 ( 9 z 2 - 32 ) ( 2 2 / 3 ( 3 + 3 ) ( ( 1 + ) z ) 2 / 3 - 4 3 z 2 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) - 20 ( 9 z 2 + 32 ) ( 4 3 z 2 / 3 + 2 2 / 3 ( 3 + 3 ) ( ( 1 + ) z ) 2 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) KelvinKer 11 3 z -1 648 2 5 6 3 1 6 z 13 3 -1 -9 3 1 3 9 z 2 160 2 2 3 3 1 2 z 1 3 -1 2 -2 1 z 1 3 AiryAi -1 1 2 3 2 3 1 z 2 3 z 5 3 3 3 1 3 9 z 2 -1 160 2 2 3 1 2 1 z 1 3 -1 2 2 3 3 3 1 2 z 1 3 AiryBi 1 2 3 2 3 1 z 2 3 z 5 3 3 3 1 3 9 z 2 160 2 2 3 1 2 1 z 1 3 -1 2 2 3 -3 3 1 2 z 1 3 AiryBi -1 1 2 3 2 3 1 z 2 3 z 5 3 18 3 1 3 z 4 9 z 2 -1 160 4 z 2 3 2 2 3 -1 3 1 2 1 z 2 3 AiryAi 1 2 3 2 3 1 z 2 3 1 z 8 3 -1 60 9 z 2 -1 32 4 z 2 3 2 2 3 -1 3 1 2 1 z 2 3 AiryAiPrime 1 2 3 2 3 1 z 2 3 120 z 5 3 9 z 2 32 2 2 3 1 -1 3 1 2 z 1 3 2 2 1 z 1 3 AiryAiPrime -1 1 2 3 2 3 1 z 2 3 1 z 4 3 -1 -1 20 9 z 2 -1 32 2 2 3 3 3 1 2 1 z 2 3 -1 4 3 1 2 z 2 3 AiryBiPrime 1 2 3 2 3 1 z 2 3 -1 20 9 z 2 32 4 3 1 2 z 2 3 2 2 3 3 3 1 2 1 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["11", "3"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", "-", "1"]], ")"]], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "9"]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["5", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["160", " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["2", "-", RowBox[List["2", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02