Formula:6428

Digital Library of Mathematical Functions ID 18.16.E8

${\displaystyle{\displaystyle\theta_{n,m}=\phi_{m}+\left(\left(\alpha^{2}-\tfrac{1}{4}\right)\frac{1-\phi_{m}\cot\phi_{m}}{2\phi_{m}}-\tfrac{1}{4}(\alpha^{2}-\beta^{2})\tan\left(\tfrac{1}{2}\phi_{m}\right)\right)\frac{1}{\rho^{2}}+\phi_{m}^{2}O\left(\frac{1}{\rho^{3}}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\cot\NVar{z}}}$: cotangent function
• ${\displaystyle{\displaystyle\tan\NVar{z}}}$: tangent function
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle\rho}}$: 18.15.E5
• ${\displaystyle{\displaystyle\theta_{n,m}}}$: zeros
• ${\displaystyle{\displaystyle\phi_{m}}}$: ϕ m
 

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