DLMF:10.32.E18 (Q3538): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / constraint
 

| ph ⁡ ( z + ζ ) | < 1 4 ⁢ π phase 𝑧 𝜁 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\left(z+\zeta\right)|<\tfrac{1}{% 4}\pi}}

|\phase@{z+\zeta}|<\tfrac{1}{4}\pi
Property / constraint: | ph ⁡ ( z + ζ ) | < 1 4 ⁢ π phase 𝑧 𝜁 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\left(z+\zeta\right)|<\tfrac{1}{% 4}\pi}} / rank
 
Normal rank

Revision as of 17:39, 30 December 2019

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DLMF:10.32.E18
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    Statements

    Defining formula
    K ν ⁡ ( z ) ⁢ K ν ⁡ ( ζ ) = 1 2 ⁢ ∫ 0 ∞ exp ⁡ ( - t 2 - z 2 + ζ 2 2 ⁢ t ) ⁢ K ν ⁡ ( z ⁢ ζ t ) ⁢ d t t , modified-Bessel-second-kind 𝜈 𝑧 modified-Bessel-second-kind 𝜈 𝜁 1 2 superscript subscript 0 𝑡 2 superscript 𝑧 2 superscript 𝜁 2 2 𝑡 modified-Bessel-second-kind 𝜈 𝑧 𝜁 𝑡 𝑡 𝑡 {\displaystyle{\displaystyle K_{\nu}\left(z\right)K_{\nu}\left(\zeta\right)=% \frac{1}{2}\int_{0}^{\infty}\exp\left(-\frac{t}{2}-\frac{z^{2}+\zeta^{2}}{2t}% \right)K_{\nu}\left(\frac{z\zeta}{t}\right)\frac{\mathrm{d}t}{t},}}
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    DLMF id
    DLMF:10.32.E18
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    constraint
    | ph ⁡ z | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}
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    | ph ⁡ ζ | < π phase 𝜁 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\zeta|<\pi}}
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    | ph ⁡ ( z + ζ ) | < 1 4 ⁢ π phase 𝑧 𝜁 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\left(z+\zeta\right)|<\tfrac{1}{% 4}\pi}}
    0 references
     
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