Formula:4048

Digital Library of Mathematical Functions ID 10.21.E44

${\displaystyle{\displaystyle J_{\nu}\left(j_{\nu,m}'\right)=\frac{h(\zeta)\mathrm{Ai}\left(a^{\prime}_{m}\right)}{\nu^{\frac{1}{3}}}\left(1+O\left(\frac{1}{\nu^{\frac{4}{3}}}\right)\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\zeta=\nu^{-\frac{2}{3}}a^{\prime}_{m}}}$

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
• ${\displaystyle{\displaystyle j_{\NVar{\nu},\NVar{m}}}}$:
• ${\displaystyle{\displaystyle a^{\prime}_{\NVar{k}}}}$:
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
• ${\displaystyle{\displaystyle h(\zeta)}}$: function (locally)
 

Resources that cite this formula

No records found.