DLMF:10.9.E16 (Q3084): Difference between revisions

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( z ± ζ ) < 0 plus-or-minus 𝑧 𝜁 0 {\displaystyle{\displaystyle\Im(z\pm\zeta)<0}}

\imagpart@@{(z\pm\zeta)}<0
Property / constraint: ( z ± ζ ) < 0 plus-or-minus 𝑧 𝜁 0 {\displaystyle{\displaystyle\Im(z\pm\zeta)<0}} / rank
 
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Revision as of 17:16, 30 December 2019

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DLMF:10.9.E16
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    Statements

    ( z + ζ z - ζ ) 1 2 ν H ν ( 2 ) ( ( 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-2-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^{(2)}_{\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.E16
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    ( z ± ζ ) < 0 plus-or-minus 𝑧 𝜁 0 {\displaystyle{\displaystyle\Im(z\pm\zeta)<0}}
    0 references