AiryAi[z] == 0 /; z == Subscript[z, k] && Element[k, Integers] && k >= 0 && Subscript[z, k] == f[3 Pi ((4 k - 1)/8)] && f[d] == (-d^(2/3)) (1 + 5/(48 d^2) - 5/(36 d^4) + 77125/(82944 d^6) - 108056875/(6967296 d^8) + 162375596875/(334430208 d^10) - 1622671914671875/(66217181184 d^12) + 150126478779573265625/ (82639042117632 d^14) - 644932726927939889453125/ (3470839768940544 d^16) + 13042116997445589075044921875/ (520200964553048064 d^18) - 569789860268573944980176052734375/ (132083753999696658432 d^20))

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> Ai </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> z </mi> <mo> &#10869; </mo> <msub> <mi> z </mi> <mi> k </mi> </msub> </mrow> <mo> &#8743; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> z </mi> <mi> k </mi> </msub> <mo> &#10869; </mo> <mrow> <mi> f </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> f </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> d </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <msup> <mi> d </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 5 </mn> <mrow> <mn> 48 </mn> <mo> &#8290; </mo> <msup> <mi> d </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> - </mo> <mfrac> <mn> 5 </mn> <mrow> <mn> 36 </mn> <mo> &#8290; </mo> <msup> <mi> d </mi> <mn> 4 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mfrac> <mn> 77125 </mn> <mrow> <mn> 82944 </mn> <mo> &#8290; </mo> <msup> <mi> d </mi> <mn> 6 </mn> </msup> </mrow> </mfrac> <mo> - </mo> <mfrac> <mn> 108056875 </mn> <mrow> <mn> 6967296 </mn> <mo> &#8290; </mo> <msup> <mi> d </mi> <mn> 8 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mfrac> <mn> 162375596875 </mn> <mrow> <mn> 334430208 </mn> <mo> &#8290; </mo> <msup> <mi> d </mi> <mn> 10 </mn> </msup> </mrow> </mfrac> <mo> - </mo> <mfrac> <mn> 1622671914671875 </mn> <mrow> <mn> 66217181184 </mn> <mo> &#8290; </mo> <msup> <mi> d </mi> <mn> 12 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mfrac> <mn> 150126478779573265625 </mn> <mrow> <mn> 82639042117632 </mn> <mo> &#8290; 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2001-10-29