DLMF:10.9#Ex9 (Q3090): Difference between revisions

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ν 1 2 , 3 2 , , | ph z | < 1 2 π formulae-sequence 𝜈 1 2 3 2 phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle\nu\neq\tfrac{1}{2},\tfrac{3}{2},\ldots,|% \operatorname{ph}z|<\tfrac{1}{2}\pi}}

\nu\neq\tfrac{1}{2},\tfrac{3}{2},\dotsc,|\phase@@{z}|<\tfrac{1}{2}\pi
Property / constraint: ν 1 2 , 3 2 , , | ph z | < 1 2 π formulae-sequence 𝜈 1 2 3 2 phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle\nu\neq\tfrac{1}{2},\tfrac{3}{2},\ldots,|% \operatorname{ph}z|<\tfrac{1}{2}\pi}} / rank
 
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Latest revision as of 17:16, 30 December 2019

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DLMF:10.9#Ex9
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    H ν ( 1 ) ( z ) = Γ ( 1 2 - ν ) ( 1 2 z ) ν π 3 2 i 1 + i ( 1 + ) e i z t ( t 2 - 1 ) ν - 1 2 d t , Hankel-H-1-Bessel-third-kind 𝜈 𝑧 Euler-Gamma 1 2 𝜈 superscript 1 2 𝑧 𝜈 superscript 𝜋 3 2 𝑖 superscript subscript 1 𝑖 limit-from 1 superscript 𝑒 𝑖 𝑧 𝑡 superscript superscript 𝑡 2 1 𝜈 1 2 𝑡 {\displaystyle{\displaystyle{H^{(1)}_{\nu}}\left(z\right)=\frac{\Gamma\left(% \tfrac{1}{2}-\nu\right)(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{3}{2}}i}\int_{1+i% \infty}^{(1+)}e^{izt}(t^{2}-1)^{\nu-\frac{1}{2}}\mathrm{d}t,}}
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    DLMF:10.9#Ex9
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    ν 1 2 , 3 2 , , | ph z | < 1 2 π formulae-sequence 𝜈 1 2 3 2 phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle\nu\neq\tfrac{1}{2},\tfrac{3}{2},\ldots,|% \operatorname{ph}z|<\tfrac{1}{2}\pi}}
    0 references