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AiryAi




Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryAi[z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself





http://functions.wolfram.com/03.05.06.0035.01









  


  








Input Form





AiryAi[z] == Subscript[F, Infinity][z] /; Subscript[F, n][z] == (1/(3^(2/3) Gamma[2/3])) Sum[(1/(Pochhammer[2/3, k] k!)) (z^3/9)^k, {k, 0, n}] - (z/(3^(1/3) Gamma[1/3])) Sum[(1/(Pochhammer[4/3, k] k!)) (z^3/9)^k, {k, 0, n}] == AiryAi[z] - (1/(3^(2/3) Gamma[2/3])) ((z^3/9)^(n + 1)/((n + 1)! Pochhammer[2/3, n + 1])) HypergeometricPFQ[{1}, {n + 2, n + 5/3}, z^3/9] + (z/(3^(1/3) Gamma[1/3])) ((z^3/9)^(n + 1)/ ((n + 1)! Pochhammer[4/3, n + 1])) HypergeometricPFQ[{1}, {n + 2, n + 7/3}, z^3/9] && Element[n, Integers] && n >= 0








Standard Form





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MathML Form







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HypergeometricPFQ </ci> <list> <cn type='integer'> 1 </cn> </list> <list> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> n </ci> <cn type='rational'> 7 <sep /> 3 </cn> </apply> </list> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 9 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02