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AiryAiPrime






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.07.06.0049.01









  


  










Input Form





AiryAiPrime[z] \[Proportional] (-(1/(2 Sqrt[6 Pi] (-z^3)^(7/12)))) ((((-1 + Sqrt[3]) z^2 + (1 + Sqrt[3]) (-z^3)^(2/3)) Cosh[(2 z^(3/2))/3] - Sqrt[z] (-z^3)^(1/6) ((1 - Sqrt[3]) z + (1 + Sqrt[3]) (-z^3)^(1/3)) Sinh[(2 z^(3/2))/3]) HypergeometricPFQ[{-(1/12), 5/12, 7/12, 13/12}, {1/2}, 9/(4 z^3)] - (7/(48 (-z^3)^(1/2))) (((1 + Sqrt[3]) z^2 + (-1 + Sqrt[3]) (-z^3)^(2/3)) Cosh[(2 z^(3/2))/3] + Sqrt[z] (-z^3)^(1/6) ((-(1 + Sqrt[3])) z + (-1 + Sqrt[3]) (-z^3)^(1/3)) Sinh[(2 z^(3/2))/3]) HypergeometricPFQ[{5/12, 11/12, 13/12, 19/12}, {3/2}, 9/(4 z^3)]) /; (Abs[z] -> Infinity)










Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 12 </cn> </apply> <cn type='rational'> 5 <sep /> 12 </cn> <cn type='rational'> 7 <sep /> 12 </cn> <cn type='rational'> 13 <sep /> 12 </cn> </list> <list> <cn type='rational'> 1 <sep /> 2 </cn> </list> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 48 </cn> <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 /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <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> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <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 /> 6 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='rational'> 5 <sep /> 12 </cn> <cn type='rational'> 11 <sep /> 12 </cn> <cn type='rational'> 13 <sep /> 12 </cn> <cn type='rational'> 19 <sep /> 12 </cn> </list> <list> <cn type='rational'> 3 <sep /> 2 </cn> </list> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <apply> <abs /> <ci> z </ci> </apply> <infinity /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02