Formula:4047

Digital Library of Mathematical Functions ID 10.21.E43

${\displaystyle{\displaystyle j_{\nu,m}'=\nu z(\zeta)+\frac{z(\zeta)(h(\zeta))^{2}C_{0}(\zeta)}{2\zeta\nu}+O\left(\frac{1}{\nu}\right),}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: 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
• ${\displaystyle{\displaystyle C_{k}(\zeta)}}$: coefficients (locally)
• ${\displaystyle{\displaystyle z(\zeta)}}$: inverse of ⁢ ζ ( z )
• ${\displaystyle{\displaystyle h(\zeta)}}$: function (locally)
 

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