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/03.17.03.0010.01

 Input Form

 KelvinBei[-(10/3), z] == (1/(18 2^(2/3) 3^(5/6) z^(10/3))) (16 Sqrt[3] (14 - 9 I z^2) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + 16 Sqrt[3] (14 + 9 I z^2) AiryAi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + (336 3^(1/6) ((1 + I) z)^(2/3) - 27 I 3^(1/6) z^2 ((1 + I) z)^(2/3)) AiryAiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (-336 3^(1/6) ((1 + I) z)^(2/3) - 27 I 3^(1/6) z^2 ((1 + I) z)^(2/3)) AiryAiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + (224 - 144 I z^2) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (224 + 144 I z^2) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + (112 3^(2/3) ((1 + I) z)^(2/3) - 9 I 3^(2/3) z^2 ((1 + I) z)^(2/3)) AiryBiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (-112 3^(2/3) ((1 + I) z)^(2/3) - 9 I 3^(2/3) z^2 ((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[RowBox[List["-", FractionBox["10", "3"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["18", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["10", "/", "3"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["16", " ", SqrtBox["3"], " ", RowBox[List["(", RowBox[List["14", "-", RowBox[List["9", " ", "\[ImaginaryI]", " ", 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["16", " ", SqrtBox["3"], " ", RowBox[List["(", RowBox[List["14", "+", 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[RowBox[List["(", RowBox[List[RowBox[List["336", " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "-", RowBox[List["27", " ", "\[ImaginaryI]", " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryAiPrime", "[", RowBox[List[RowBox[List["-", 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RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "112"]], " ", 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", " ", "\[ImaginaryI]", " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", "2"], " ", 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 - 10 3 ( z ) 1 18 2 2 / 3 3 5 / 6 z 10 / 3 ( 16 3 ( 9 z 2 + 14 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 16 3 ( 14 - 9 z 2 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + ( - 336 3 6 ( ( 1 + ) z ) 2 / 3 - 27 3 6 z 2 ( ( 1 + ) z ) 2 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + ( 336 3 6 ( ( 1 + ) z ) 2 / 3 - 27 3 6 z 2 ( ( 1 + ) z ) 2 / 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + ( 144 z 2 + 224 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + ( 224 - 144 z 2 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + ( - 112 3 2 / 3 ( ( 1 + ) z ) 2 / 3 - 9 3 2 / 3 z 2 ( ( 1 + ) z ) 2 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + ( 112 3 2 / 3 ( ( 1 + ) z ) 2 / 3 - 9 3 2 / 3 z 2 ( ( 1 + ) z ) 2 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) KelvinBei -1 10 3 z 1 18 2 2 3 3 5 6 z 10 3 -1 16 3 1 2 9 z 2 14 AiryAi 1 2 3 2 3 1 z 2 3 16 3 1 2 14 -1 9 z 2 AiryAi -1 1 2 3 2 3 1 z 2 3 -336 3 1 6 1 z 2 3 -1 27 3 1 6 z 2 1 z 2 3 AiryAiPrime 1 2 3 2 3 1 z 2 3 336 3 1 6 1 z 2 3 -1 27 3 1 6 z 2 1 z 2 3 AiryAiPrime -1 1 2 3 2 3 1 z 2 3 144 z 2 224 AiryBi 1 2 3 2 3 1 z 2 3 224 -1 144 z 2 AiryBi -1 1 2 3 2 3 1 z 2 3 -112 3 2 3 1 z 2 3 -1 9 3 2 3 z 2 1 z 2 3 AiryBiPrime 1 2 3 2 3 1 z 2 3 112 3 2 3 1 z 2 3 -1 9 3 2 3 z 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["KelvinBei", "[", RowBox[List[RowBox[List["-", FractionBox["10", "3"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["16", " ", SqrtBox["3"], " ", RowBox[List["(", RowBox[List["14", "-", RowBox[List["9", " ", "\[ImaginaryI]", " ", 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["16", " ", SqrtBox["3"], " ", RowBox[List["(", RowBox[List["14", "+", RowBox[List["9", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["AiryAi", "[", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02