DLMF:13.20.E14 (Q4603)

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DLMF:13.20.E14
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    Statements

    test
    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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    DLMF id
    DLMF:13.20.E14
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    constraint
    2 ⁢ κ - 2 ⁢ κ 2 - μ 2 ≤ x ≤ 2 ⁢ κ + 2 ⁢ κ 2 - μ 2 2 𝜅 2 superscript 𝜅 2 superscript 𝜇 2 𝑥 2 𝜅 2 superscript 𝜅 2 superscript 𝜇 2 {\displaystyle{\displaystyle 2\kappa-2\sqrt{\kappa^{2}-\mu^{2}}\leq x\leq 2% \kappa+2\sqrt{\kappa^{2}-\mu^{2}}}}
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