DLMF:10.61.E2 (Q3791): Difference between revisions

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Property / Symbols defined: Kelvin function / rank
 
Normal rank

Revision as of 16:13, 30 December 2019

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DLMF:10.61.E2
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    ker ν ⁡ x + i ⁢ kei ν ⁡ x = e - ν ⁢ π ⁢ i / 2 ⁢ K ν ⁡ ( x ⁢ e π ⁢ i / 4 ) = 1 2 ⁢ π ⁢ i ⁢ H ν ( 1 ) ⁡ ( x ⁢ e 3 ⁢ π ⁢ i / 4 ) = - 1 2 ⁢ π ⁢ i ⁢ e - ν ⁢ π ⁢ i ⁢ H ν ( 2 ) ⁡ ( x ⁢ e - π ⁢ i / 4 ) . Kelvin-ker 𝜈 𝑥 𝑖 Kelvin-kei 𝜈 𝑥 superscript 𝑒 𝜈 𝜋 𝑖 2 modified-Bessel-second-kind 𝜈 𝑥 superscript 𝑒 𝜋 𝑖 4 1 2 𝜋 𝑖 Hankel-H-1-Bessel-third-kind 𝜈 𝑥 superscript 𝑒 3 𝜋 𝑖 4 1 2 𝜋 𝑖 superscript 𝑒 𝜈 𝜋 𝑖 Hankel-H-2-Bessel-third-kind 𝜈 𝑥 superscript 𝑒 𝜋 𝑖 4 {\displaystyle{\displaystyle\operatorname{ker}_{\nu}x+i\operatorname{kei}_{\nu% }x=e^{-\nu\pi i/2}K_{\nu}\left(xe^{\pi i/4}\right)=\tfrac{1}{2}\pi i{H^{(1)}_{% \nu}}\left(xe^{3\pi i/4}\right)=-\tfrac{1}{2}\pi ie^{-\nu\pi i}{H^{(2)}_{\nu}}% \left(xe^{-\pi i/4}\right).}}
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    DLMF:10.61.E2
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