DLMF:10.19#Ex21 (Q3239)

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DLMF:10.19#Ex21
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    Y ν ( ν + a ν 1 3 ) 2 2 3 ν 2 3 Bi ( - 2 1 3 a ) k = 0 R k ( a ) ν 2 k / 3 - 2 1 3 ν 4 3 Bi ( - 2 1 3 a ) k = 0 S k ( a ) ν 2 k / 3 , asymptotic-expansion diffop Bessel-Y-Weber 𝜈 1 𝜈 𝑎 superscript 𝜈 1 3 superscript 2 2 3 superscript 𝜈 2 3 diffop Airy-Bi 1 superscript 2 1 3 𝑎 superscript subscript 𝑘 0 subscript 𝑅 𝑘 𝑎 superscript 𝜈 2 𝑘 3 superscript 2 1 3 superscript 𝜈 4 3 Airy-Bi superscript 2 1 3 𝑎 superscript subscript 𝑘 0 subscript 𝑆 𝑘 𝑎 superscript 𝜈 2 𝑘 3 {\displaystyle{\displaystyle Y_{\nu}'\left(\nu+a\nu^{\frac{1}{3}}\right)\sim% \frac{2^{\frac{2}{3}}}{\nu^{\frac{2}{3}}}\mathrm{Bi}'\left(-2^{\frac{1}{3}}a% \right)\sum_{k=0}^{\infty}\frac{R_{k}(a)}{\nu^{2k/3}}-\frac{2^{\frac{1}{3}}}{% \nu^{\frac{4}{3}}}\mathrm{Bi}\left(-2^{\frac{1}{3}}a\right)\sum_{k=0}^{\infty}% \frac{S_{k}(a)}{\nu^{2k/3}},}}
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