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AiryBi






Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryBi[z] > Series representations > Asymptotic series expansions > Expansions for any z in exponential form > Using exponential function with branch cut-free arguments





http://functions.wolfram.com/03.06.06.0043.01









  


  










Input Form





AiryBi[z] \[Proportional] (1/((-z^3)^(5/12) (8 Sqrt[Pi]))) ((Sqrt[2]/z^(3/2)) (((-1 + Sqrt[3]) z^(5/2) + (1 + Sqrt[3]) z^(3/2) (-z^3)^(1/3) - (1 + Sqrt[3]) z Sqrt[-z^3] - (-1 + Sqrt[3]) (-z^3)^(5/6))/E^((2 z^(3/2))/3) + E^((2 z^(3/2))/3) ((-1 + Sqrt[3]) z^(5/2) + (1 + Sqrt[3]) z^(3/2) (-z^3)^(1/3) + (1 + Sqrt[3]) z Sqrt[-z^3] + (-1 + Sqrt[3]) (-z^3)^(5/6))) (1 + 385/(4608 z^3) + 37182145/(127401984 z^6) + 5849680962125/(1761205026816 z^9) + O[1/z^12]) + (5/(24 Sqrt[2] z^3)) (((-(-1 + Sqrt[3])) z^(5/2) - (1 + Sqrt[3]) z^(3/2) (-z^3)^(1/3) + (1 + Sqrt[3]) z Sqrt[-z^3] + (-1 + Sqrt[3]) (-z^3)^(5/6))/E^((2 z^(3/2))/3) + E^((2 z^(3/2))/3) ((-1 + Sqrt[3]) z^(5/2) + (1 + Sqrt[3]) z^(3/2) (-z^3)^(1/3) + (1 + Sqrt[3]) z Sqrt[-z^3] + (-1 + Sqrt[3]) (-z^3)^(5/6))) (1 + 17017/(13824 z^3) + 1078282205/(127401984 z^6) + 253541886272675/(1761205026816 z^9) + O[1/z^12])) /; (Abs[z] -> Infinity)










Standard Form





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MathML Form







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<msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mn> 3 </mn> </mroot> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> </msqrt> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> 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Rule Form





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





2007-05-02





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