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; }

 KelvinBei

 http://functions.wolfram.com/03.17.03.0029.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["KelvinBei", "[", RowBox[List[FractionBox["5", "3"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["5", "/", "3"]]]]], RowBox[List["3", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["10", "/", "3"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["9", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["4", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["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["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["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["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"]]]]], "]"]]]], "+", 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["8", " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", RowBox[List["AiryAiPrime", "[", 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["3", " ", "\[ImaginaryI]", " ", 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"]]]]], "]"]]]], "+", RowBox[List[SqrtBox["3"], " ", RowBox[List["(", RowBox[List[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["\[ImaginaryI]", " ", 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

 bei 5 3 ( z ) - 1 4 z 5 / 3 3 2 2 / 3 3 5 / 6 ( ( 1 + ) z ) 10 / 3 ( 9 ( ( 1 + ) z ) 4 / 3 ( 3 Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + ( 3 Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) + Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) - 8 3 6 ( 3 Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 3 Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 3 ( Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) ) ) KelvinBei 5 3 z -1 1 4 z 5 3 3 2 2 3 3 5 6 1 z 10 3 -1 9 1 z 4 3 3 1 2 AiryAi -1 1 2 3 2 3 1 z 2 3 3 1 2 AiryAi 1 2 3 2 3 1 z 2 3 AiryBi 1 2 3 2 3 1 z 2 3 AiryBi -1 1 2 3 2 3 1 z 2 3 -1 8 3 1 6 3 AiryAiPrime 1 2 3 2 3 1 z 2 3 3 AiryAiPrime -1 1 2 3 2 3 1 z 2 3 3 1 2 AiryBiPrime 1 2 3 2 3 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["KelvinBei", "[", RowBox[List[FractionBox["5", "3"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["5", "/", "3"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["9", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["4", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["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["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["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["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"]]]]], "]"]]]], "+", 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["8", " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", RowBox[List["AiryAiPrime", "[", 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["3", " ", "\[ImaginaryI]", " ", 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"]]]]], "]"]]]], "+", RowBox[List[SqrtBox["3"], " ", RowBox[List["(", RowBox[List[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["\[ImaginaryI]", " ", 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["3", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["10", "/", "3"]]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2007-05-02