DLMF:10.21.E42 (Q3349): Difference between revisions

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Property / constraint
 

ζ = ν - 2 3 a m 𝜁 superscript 𝜈 2 3 zero-Airy-Ai 𝑚 {\displaystyle{\displaystyle\zeta=\nu^{-\frac{2}{3}}a_{m}}}

\zeta=\nu^{-\frac{2}{3}}\zAirya{m}
Property / constraint: ζ = ν - 2 3 a m 𝜁 superscript 𝜈 2 3 zero-Airy-Ai 𝑚 {\displaystyle{\displaystyle\zeta=\nu^{-\frac{2}{3}}a_{m}}} / rank
 
Normal rank

Revision as of 16:18, 30 December 2019

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DLMF:10.21.E42
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    Statements

    J ν ( j ν , m ) = - 2 ν 2 3 Ai ( a m ) z ( ζ ) h ( ζ ) ( 1 + O ( 1 ν 2 ) ) , diffop Bessel-J 𝜈 1 zero-Bessel-J 𝜈 𝑚 2 superscript 𝜈 2 3 diffop Airy-Ai 1 zero-Airy-Ai 𝑚 𝑧 𝜁 𝜁 1 Big-O 1 superscript 𝜈 2 {\displaystyle{\displaystyle J_{\nu}'\left(j_{\nu,m}\right)=-\frac{2}{\nu^{% \frac{2}{3}}}\frac{\mathrm{Ai}'\left(a_{m}\right)}{z(\zeta)h(\zeta)}\left(1+O% \left(\frac{1}{\nu^{2}}\right)\right),}}
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    ζ = ν - 2 3 a m 𝜁 superscript 𝜈 2 3 zero-Airy-Ai 𝑚 {\displaystyle{\displaystyle\zeta=\nu^{-\frac{2}{3}}a_{m}}}
    0 references