Formula:4004

Digital Library of Mathematical Functions ID 10.21.E23

${\displaystyle{\displaystyle\mathscr{C}_{\nu}'\left(\rho_{\nu}(t)\right)\sim\frac{(2/\nu)^{\frac{2}{3}}}{\pi M\left(-2^{\frac{1}{3}}\alpha\right)}\sum_{k=0}^{\infty}\frac{\beta_{k}}{\nu^{2k/3}},}}$

Symbols List

• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: cylinder function
• ${\displaystyle{\displaystyle M\left(\NVar{z}\right)}}$: Airy modulus function
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
• ${\displaystyle{\displaystyle\rho_{\nu}(t)}}$: zero of cylinder function
• ${\displaystyle{\displaystyle\alpha}}$: coefficients (locally)
• ${\displaystyle{\displaystyle\beta}}$: coefficients
 

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