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; }

 KelvinKei

 http://functions.wolfram.com/03.19.03.0027.01

 Input Form

 KelvinKei[5/3, z] == ((-1)^(2/3) Pi z^(2/3) (18 3^(1/3) ((-I + Sqrt[3]) z^(2/3) - 2^(2/3) ((1 + I) z)^(2/3)) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + 9 3^(1/3) (4 (-1)^(1/3) 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)^(5/3)) (48 I z^(2/3) ((1 - I) 2^(2/3) z^(1/3) + (1 + I Sqrt[3]) ((1 + I) z)^(1/3)) AiryAiPrime[ (-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)]) + (1/z^4) (6 ((1 + I) z)^(8/3) ((2 - 2 I) (-1)^(7/12) Sqrt[2] 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)]) - 6 (-2 (-3)^(5/6) z^(2/3) + 2^(2/3) 3^(5/6) ((1 + I) z)^(2/3)) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (1/z^2) (3 I (4 (-3)^(5/6) z^(8/3) - I (3/2)^(1/3) (-3 I + Sqrt[3]) ((1 + I) z)^(8/3)) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)]) + (16 Sqrt[6] (2^(1/6) z^(1/3) - (-1)^(7/12) ((1 + I) z)^(1/3)) AiryBiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)])/ (z^(1/3) ((1 + I) z)^(2/3)) + (1/(z^(1/3) ((1 + I) z)^(2/3))) (8 Sqrt[2] (2^(1/6) (-3 - I Sqrt[3]) z^(1/3) + 2 (-1)^(1/12) Sqrt[3] ((1 + I) z)^(1/3)) AiryBiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)])))/ (36 2^(5/6) 3^(1/6) ((1 + I) z)^(5/3))

 Standard Form

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RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "12"]]], " ", SqrtBox["3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["1", "/", "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["36", " ", SuperscriptBox["2", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["5", "/", "3"]]]]], ")"]]]]]]]]

 MathML Form

 kei 5 3 ( z ) ( - 1 ) 2 / 3 π z 2 / 3 36 2 5 / 6 3 6 ( ( 1 + ) z ) 5 / 3 ( 48 ( 2 2 / 3 ( 1 - ) z 3 + ( 1 + 3 ) ( 1 + ) z 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 / 3 ( ( 1 + ) z ) 5 / 3 + 9 3 3 ( 4 - 1 3 z 2 / 3 + 2 2 / 3 ( + 3 ) ( ( 1 + ) z ) 2 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 18 3 3 ( ( - + 3 ) z 2 / 3 - 2 2 / 3 ( ( 1 + ) z ) 2 / 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 6 ( ( 1 + ) z ) 8 / 3 ( ( - 1 ) 7 / 12 2 ( 2 - 2 ) z 2 / 3 + 2 2 / 3 ( + 3 ) ( ( 1 + ) z ) 2 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 4 + 3 ( 4 ( - 3 ) 5 / 6 z 8 / 3 - 3 2 3 ( - 3 + 3 ) ( ( 1 + ) z ) 8 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 - 6 ( 2 2 / 3 3 5 / 6 ( ( 1 + ) z ) 2 / 3 - 2 ( - 3 ) 5 / 6 z 2 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 8 2 ( 2 6 ( - 3 - 3 ) z 3 + 2 - 1 12 3 ( 1 + ) z 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 ( ( 1 + ) z ) 2 / 3 + 16 6 ( 2 6 z 3 - ( - 1 ) 7 / 12 ( 1 + ) z 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 ( ( 1 + ) z ) 2 / 3 ) KelvinKei 5 3 z -1 2 3 z 2 3 36 2 5 6 3 1 6 1 z 5 3 -1 48 2 2 3 1 -1 z 1 3 1 3 1 2 1 z 1 3 AiryAiPrime -1 1 2 3 2 3 1 z 2 3 z 2 3 1 z 5 3 -1 9 3 1 3 4 -1 1 3 z 2 3 2 2 3 3 1 2 1 z 2 3 AiryAi 1 2 3 2 3 1 z 2 3 18 3 1 3 -1 3 1 2 z 2 3 -1 2 2 3 1 z 2 3 AiryAi -1 1 2 3 2 3 1 z 2 3 6 1 z 8 3 -1 7 12 2 1 2 2 -2 z 2 3 2 2 3 3 1 2 1 z 2 3 AiryAiPrime 1 2 3 2 3 1 z 2 3 z 4 -1 3 4 -3 5 6 z 8 3 -1 3 2 1 3 -3 3 1 2 1 z 8 3 AiryBi 1 2 3 2 3 1 z 2 3 z 2 -1 -1 6 2 2 3 3 5 6 1 z 2 3 -1 2 -3 5 6 z 2 3 AiryBi -1 1 2 3 2 3 1 z 2 3 8 2 1 2 2 1 6 -3 -1 3 1 2 z 1 3 2 -1 1 12 3 1 2 1 z 1 3 AiryBiPrime 1 2 3 2 3 1 z 2 3 z 1 3 1 z 2 3 -1 16 6 1 2 2 1 6 z 1 3 -1 -1 7 12 1 z 1 3 AiryBiPrime -1 1 2 3 2 3 1 z 2 3 z 1 3 1 z 2 3 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKei", "[", RowBox[List[FractionBox["5", "3"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "3"]]], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["18", " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "-", RowBox[List[SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryAi", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02