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AiryAi






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.05.06.0021.01









  


  










Input Form





AiryAi[z] \[Proportional] (1/((-z^3)^(5/12) (2 Sqrt[3 Pi]))) (((-1)^(1/12) ((-z^3)^(1/3) - (-1)^(1/3) z) (Sum[((Pochhammer[1/6, k] Pochhammer[5/6, k])/k!) ((3 I)/(4 Sqrt[-z^3]))^k, {k, 0, n}] + O[1/z^(3 ((n + 1)/2))]))/ E^((2/3) I Sqrt[-z^3]) + (E^((2/3) I Sqrt[-z^3]) ((-z^3)^(1/3) + (-1)^(2/3) z) (Sum[((Pochhammer[1/6, k] Pochhammer[5/6, k])/k!) (-((3 I)/(4 Sqrt[-z^3])))^k, {k, 0, n}] + O[1/z^(3 ((n + 1)/2))]))/ (-1)^12^(-1)) /; (Abs[z] -> Infinity) && Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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-1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <times /> <apply> <ci> Pochhammer </ci> <cn type='rational'> 1 <sep /> 6 </cn> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 5 <sep /> 6 </cn> <ci> k </ci> </apply> <apply> <power /> <apply> <factorial /> <ci> k </ci> </apply> <cn 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Rule Form





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





2003-08-21





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