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/03.17.03.0030.01

 Input Form

 KelvinBei[7/3, z] == ((-1)^(1/4)/(6 2^(1/3) 3^(5/6) z^(5/3) ((1 + I) z)^(2/3))) ((-Sqrt[3]) (16 I + 9 z^2) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + Sqrt[3] (-16 - 9 I z^2) AiryAi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] - 24 I 3^(1/6) ((1 + I) z)^(2/3) AiryAiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + 24 3^(1/6) ((1 + I) z)^(2/3) AiryAiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + (16 I + 9 z^2) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (16 + 9 I z^2) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + 8 I 3^(2/3) ((1 + I) z)^(2/3) AiryBiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] - 8 3^(2/3) ((1 + I) z)^(2/3) AiryBiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["KelvinBei", "[", RowBox[List[FractionBox["7", "3"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " "]], RowBox[List["6", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["5", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SqrtBox["3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["16", " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", 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[SqrtBox["3"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "16"]], "-", RowBox[List["9", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", 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["24", " ", "\[ImaginaryI]", " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "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["24", " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "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"]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["16", " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", 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[RowBox[List["(", RowBox[List["16", "+", RowBox[List["9", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", 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", " ", "\[ImaginaryI]", " ", SuperscriptBox["3", RowBox[List["2", "/", "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["8", " ", SuperscriptBox["3", RowBox[List["2", "/", "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

 bei 7 3 ( z ) 1 6 2 3 3 5 / 6 z 5 / 3 ( ( 1 + ) z ) 2 / 3 ( - 1 4 ( 24 3 6 Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 2 / 3 - 24 3 6 Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 2 / 3 - 8 3 2 / 3 Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 2 / 3 + 8 3 2 / 3 Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 2 / 3 + 3 ( - 9 z 2 - 16 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) - 3 ( 9 z 2 + 16 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + ( 9 z 2 + 16 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + ( 9 z 2 + 16 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) ) KelvinBei 7 3 z 1 6 2 1 3 3 5 6 z 5 3 1 z 2 3 -1 -1 1 4 24 3 1 6 AiryAiPrime 1 2 3 2 3 1 z 2 3 1 z 2 3 -1 24 3 1 6 AiryAiPrime -1 1 2 3 2 3 1 z 2 3 1 z 2 3 -1 8 3 2 3 AiryBiPrime 1 2 3 2 3 1 z 2 3 1 z 2 3 8 3 2 3 AiryBiPrime -1 1 2 3 2 3 1 z 2 3 1 z 2 3 3 1 2 -9 z 2 -16 AiryAi 1 2 3 2 3 1 z 2 3 -1 3 1 2 9 z 2 16 AiryAi -1 1 2 3 2 3 1 z 2 3 9 z 2 16 AiryBi 1 2 3 2 3 1 z 2 3 9 z 2 16 AiryBi -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["7", "3"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SqrtBox["3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["16", " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", 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[SqrtBox["3"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "16"]], "-", RowBox[List["9", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", 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["24", " ", "\[ImaginaryI]", " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "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["24", " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "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"]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["16", " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", 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[RowBox[List["(", RowBox[List["16", "+", RowBox[List["9", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", 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", " ", "\[ImaginaryI]", " ", SuperscriptBox["3", RowBox[List["2", "/", "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["8", " ", SuperscriptBox["3", RowBox[List["2", "/", "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"]]]]], "]"]]]]]], ")"]]]], RowBox[List["6", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["5", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]]]]]]]

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

 2007-05-02