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/03.20.03.0012.01

 Input Form

 KelvinKer[-(5/3), z] == (1/(36 2^(1/3) 3^(1/6))) ((-1)^(1/4) Pi z^(5/3) (3 I 2^(2/3) 3^(5/6) (3 + I Sqrt[3]) ((1 + I) z)^(4/3) ((-(1/2))^(2/3)/(2 z^(10/3)) + (-1)^(5/6)/((1 + I) z)^(10/3)) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] - 9 3^(1/3) ((1 + I) z)^(4/3) (-((-1)^(1/6)/z^(10/3)) + 1/((-1)^(1/4) z)^(10/3)) AiryAi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + (24 ((-1)^(1/3) z^(2/3) - I ((-1)^(1/4) z)^(2/3)) AiryAiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)])/z^4 - (24 ((-1)^(1/6) z^(2/3) + ((-1)^(1/4) z)^(2/3)) AiryAiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)])/z^4 + (1/(2^(1/3) z^4)) (3 I 3^(5/6) ((1 + I) z)^(4/3) ((-(-1)^(5/6)) 2^(1/3) z^(2/3) + ((1 + I) z)^(2/3)) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)]) + (1/(2^(1/3) z^4)) (3 3^(5/6) ((1 + I) z)^(4/3) ((-(-1)^(1/6)) 2^(1/3) z^(2/3) + ((1 + I) z)^(2/3)) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)]) - (8 Sqrt[3] ((-1)^(1/3) z^(2/3) + I ((-1)^(1/4) z)^(2/3)) AiryBiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)])/z^4 + (8 Sqrt[3] ((-1)^(1/6) z^(2/3) - ((-1)^(1/4) z)^(2/3)) AiryBiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)])/z^4))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["KelvinKer", "[", RowBox[List[RowBox[List["-", FractionBox["5", "3"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["36", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]]]]], RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["5", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", "\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["5", "/", "6"]]], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["4", "/", "3"]]], " ", RowBox[List["(", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["1", "2"]]], ")"]], RowBox[List["2", "/", "3"]]], RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["10", "/", "3"]]]]]], "+", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "6"]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["10", "/", "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", " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["4", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "6"]]], SuperscriptBox["z", RowBox[List["10", "/", "3"]]]]]], "+", FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["10", "/", "3"]]]]]], ")"]], " ", RowBox[List["AiryAi", "[", 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"]]]]], "]"]]]], "+", FractionBox[RowBox[List["24", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], 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"3"]]]]], ")"]], " ", RowBox[List["AiryAiPrime", "[", 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"]]]]], "]"]]]], SuperscriptBox["z", "4"]], "+", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", "4"]]]], RowBox[List["3", " ", "\[ImaginaryI]", " ", SuperscriptBox["3", RowBox[List["5", "/", "6"]]], " ", 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["-", "1"]], ")"]], RowBox[List["5", "/", "6"]]]]], " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], ")"]], " ", RowBox[List["AiryBi", "[", 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[FractionBox["1", RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", "4"]]]], RowBox[List["3", " ", SuperscriptBox["3", RowBox[List["5", "/", "6"]]], " ", 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["-", "1"]], ")"]], RowBox[List["1", "/", "6"]]]]], " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "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"]]]]], "]"]]]]]], "-", FractionBox[RowBox[List["8", " ", SqrtBox["3"], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "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"]]]]], "]"]]]], SuperscriptBox["z", "4"]], "+", FractionBox[RowBox[List["8", " ", SqrtBox["3"], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], 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["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"]]]]], "]"]]]], SuperscriptBox["z", "4"]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 ker - 5 3 ( z ) - 1 4 π z 5 / 3 36 2 3 3 6 ( - 9 3 3 ( 1 ( - 1 4 z ) 10 / 3 - - 1 6 z 10 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 4 / 3 + 3 2 2 / 3 3 5 / 6 ( 3 + 3 ) ( ( - 1 2 ) 2 / 3 2 z 10 / 3 + ( - 1 ) 5 / 6 ( ( 1 + ) z ) 10 / 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 4 / 3 + 3 3 5 / 6 ( ( ( 1 + ) z ) 2 / 3 - - 1 6 2 3 z 2 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 4 / 3 2 3 z 4 + 3 3 5 / 6 ( ( ( 1 + ) z ) 2 / 3 - ( - 1 ) 5 / 6 2 3 z 2 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 4 / 3 2 3 z 4 + 24 ( - 1 3 z 2 / 3 - ( - 1 4 z ) 2 / 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 4 + 8 3 ( - 1 6 z 2 / 3 - ( - 1 4 z ) 2 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 4 - 24 ( - 1 6 z 2 / 3 + ( - 1 4 z ) 2 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 4 - 8 3 ( - 1 3 z 2 / 3 + ( - 1 4 z ) 2 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 4 ) KelvinKer -1 5 3 z -1 1 4 z 5 3 36 2 1 3 3 1 6 -1 -9 3 1 3 1 -1 1 4 z 10 3 -1 -1 -1 1 6 z 10 3 -1 AiryAi 1 2 3 2 3 1 z 2 3 1 z 4 3 3 2 2 3 3 5 6 3 3 1 2 -1 1 2 2 3 2 z 10 3 -1 -1 5 6 1 z 10 3 -1 AiryAi -1 1 2 3 2 3 1 z 2 3 1 z 4 3 3 3 5 6 1 z 2 3 -1 -1 1 6 2 1 3 z 2 3 AiryBi 1 2 3 2 3 1 z 2 3 1 z 4 3 2 1 3 z 4 -1 3 3 5 6 1 z 2 3 -1 -1 5 6 2 1 3 z 2 3 AiryBi -1 1 2 3 2 3 1 z 2 3 1 z 4 3 2 1 3 z 4 -1 24 -1 1 3 z 2 3 -1 -1 1 4 z 2 3 AiryAiPrime -1 1 2 3 2 3 1 z 2 3 z 4 -1 8 3 1 2 -1 1 6 z 2 3 -1 -1 1 4 z 2 3 AiryBiPrime 1 2 3 2 3 1 z 2 3 z 4 -1 -1 24 -1 1 6 z 2 3 -1 1 4 z 2 3 AiryAiPrime 1 2 3 2 3 1 z 2 3 z 4 -1 -1 8 3 1 2 -1 1 3 z 2 3 -1 1 4 z 2 3 AiryBiPrime -1 1 2 3 2 3 1 z 2 3 z 4 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKer", "[", RowBox[List[RowBox[List["-", FractionBox["5", "3"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["5", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", "\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["5", "/", "6"]]], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["4", "/", "3"]]], " ", RowBox[List["(", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["1", "2"]]], ")"]], RowBox[List["2", "/", "3"]]], RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["10", "/", "3"]]]]]], "+", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "6"]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["10", "/", "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", " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["4", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02