DLMF:10.9.E15 (Q3083)

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DLMF:10.9.E15
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    ( z + ζ z - ζ ) 1 2 ν H ν ( 1 ) ( ( z 2 - ζ 2 ) 1 2 ) = 1 π i e - 1 2 ν π i - e i z cosh t + i ζ sinh t - ν t d t , superscript 𝑧 𝜁 𝑧 𝜁 1 2 𝜈 Hankel-H-1-Bessel-third-kind 𝜈 superscript superscript 𝑧 2 superscript 𝜁 2 1 2 1 𝜋 𝑖 superscript 𝑒 1 2 𝜈 𝜋 𝑖 superscript subscript superscript 𝑒 𝑖 𝑧 𝑡 𝑖 𝜁 𝑡 𝜈 𝑡 𝑡 {\displaystyle{\displaystyle\left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}% \nu}{H^{(1)}_{\nu}}\left((z^{2}-\zeta^{2})^{\frac{1}{2}}\right)=\frac{1}{\pi i% }e^{-\frac{1}{2}\nu\pi i}\int_{-\infty}^{\infty}e^{iz\cosh t+i\zeta\sinh t-\nu t% }\mathrm{d}t,}}
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    DLMF:10.9.E15
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