Formula:4046

Digital Library of Mathematical Functions ID 10.21.E42

${\displaystyle{\displaystyle J_{\nu}'\left(j_{\nu,m}\right)=-\frac{2}{\nu^{\frac{2}{3}}}\frac{\mathrm{Ai}'\left(a_{m}\right)}{z(\zeta)h(\zeta)}\left(1+O\left(\frac{1}{\nu^{2}}\right)\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\zeta=\nu^{-\frac{2}{3}}a_{m}}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle a_{\NVar{k}}}}$:
• ${\displaystyle{\displaystyle j_{\NVar{\nu},\NVar{m}}}}$:
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
• ${\displaystyle{\displaystyle z(\zeta)}}$: inverse of ⁢ ζ ( z )
• ${\displaystyle{\displaystyle h(\zeta)}}$: function (locally)
 

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