DLMF:19.9#Ex5 (Q6262)

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DLMF:19.9#Ex5
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    Defining formula
    U = 1 2 ⁢ arctanh ⁡ ( sin ⁡ ϕ ) + 1 2 ⁢ k - 1 ⁢ arctanh ⁡ ( k ⁢ sin ⁡ ϕ ) . 𝑈 1 2 hyperbolic-inverse-tangent italic-ϕ 1 2 superscript 𝑘 1 hyperbolic-inverse-tangent 𝑘 italic-ϕ {\displaystyle{\displaystyle U=\tfrac{1}{2}\operatorname{arctanh}\left(\sin% \phi\right)+\tfrac{1}{2}k^{-1}\operatorname{arctanh}\left(k\sin\phi\right).}}
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    DLMF:19.9#Ex5
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