DLMF:9.12.E22 (Q2950): Difference between revisions

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Property / constraint
 

| ph z | < 1 3 π phase 𝑧 1 3 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{3}\pi}}

|\phase@@{z}|<\tfrac{1}{3}\pi
Property / constraint: | ph z | < 1 3 π phase 𝑧 1 3 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{3}\pi}} / rank
 
Normal rank

Revision as of 17:14, 30 December 2019

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DLMF:9.12.E22
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    Statements

    Hi ( - z ) = 4 z 2 3 3 / 2 π 2 0 K 1 / 3 ( t ) ζ 2 + t 2 d t , Scorer-Hi 𝑧 4 superscript 𝑧 2 superscript 3 3 2 superscript 𝜋 2 superscript subscript 0 modified-Bessel-second-kind 1 3 𝑡 superscript 𝜁 2 superscript 𝑡 2 𝑡 {\displaystyle{\displaystyle\mathrm{Hi}\left(-z\right)=\frac{4z^{2}}{3^{3/2}% \pi^{2}}\int_{0}^{\infty}\frac{K_{1/3}\left(t\right)}{\zeta^{2}+t^{2}}\mathrm{% d}t,}}
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    | ph z | < 1 3 π phase 𝑧 1 3 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{3}\pi}}
    0 references