DLMF:13.20.E14 (Q4603)

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DLMF:13.20.E14
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    ζ α 2 - ζ 2 + α 2 arcsin ( ζ α ) = X μ + 2 κ μ arctan ( x - 2 κ X ) - 2 arctan ( κ x - 2 μ 2 μ X ) , 𝜁 superscript 𝛼 2 superscript 𝜁 2 superscript 𝛼 2 𝜁 𝛼 𝑋 𝜇 2 𝜅 𝜇 𝑥 2 𝜅 𝑋 2 𝜅 𝑥 2 superscript 𝜇 2 𝜇 𝑋 {\displaystyle{\displaystyle\zeta\sqrt{\alpha^{2}-\zeta^{2}}+\alpha^{2}% \operatorname{arcsin}\left(\frac{\zeta}{\alpha}\right)=\frac{X}{\mu}+\frac{2% \kappa}{\mu}\operatorname{arctan}\left(\frac{x-2\kappa}{X}\right)-2% \operatorname{arctan}\left(\frac{\kappa x-2\mu^{2}}{\mu X}\right),}}
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