DLMF:10.32.E10 (Q3530): Difference between revisions

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Property / constraint
 

| ph z | < 1 4 π phase 𝑧 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{4}\pi}}

|\phase@@{z}|<\tfrac{1}{4}\pi
Property / constraint: | ph z | < 1 4 π phase 𝑧 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{4}\pi}} / rank
 
Normal rank

Revision as of 17:38, 30 December 2019

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DLMF:10.32.E10
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    Statements

    K ν ( z ) = 1 2 ( 1 2 z ) ν 0 exp ( - t - z 2 4 t ) d t t ν + 1 , modified-Bessel-second-kind 𝜈 𝑧 1 2 superscript 1 2 𝑧 𝜈 superscript subscript 0 𝑡 superscript 𝑧 2 4 𝑡 𝑡 superscript 𝑡 𝜈 1 {\displaystyle{\displaystyle K_{\nu}\left(z\right)=\tfrac{1}{2}(\tfrac{1}{2}z)% ^{\nu}\int_{0}^{\infty}\exp\left(-t-\frac{z^{2}}{4t}\right)\frac{\mathrm{d}t}{% t^{\nu+1}},}}
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    | ph z | < 1 4 π phase 𝑧 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{4}\pi}}
    0 references