DLMF:9.7.E13 (Q2820): Difference between revisions

From DRMF
Jump to navigation Jump to search
Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
Property / constraint
 

| ph z | 2 3 π - δ phase 𝑧 2 3 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{2}{3}\pi-\delta}}

|\phase@@{z}|\leq\tfrac{2}{3}\pi-\delta
Property / constraint: | ph z | 2 3 π - δ phase 𝑧 2 3 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{2}{3}\pi-\delta}} / rank
 
Normal rank

Revision as of 17:13, 30 December 2019

No description defined
Language Label Description Also known as
English
DLMF:9.7.E13
No description defined

    Statements

    Bi ( z e ± π i / 3 ) 2 π e ± π i / 6 z 1 / 4 ( cos ( ζ - 1 4 π 1 2 i ln 2 ) k = 0 ( - 1 ) k u 2 k ζ 2 k + sin ( ζ - 1 4 π 1 2 i ln 2 ) k = 0 ( - 1 ) k u 2 k + 1 ζ 2 k + 1 ) , asymptotic-expansion Airy-Bi 𝑧 superscript 𝑒 plus-or-minus 𝜋 𝑖 3 2 𝜋 superscript 𝑒 plus-or-minus 𝜋 𝑖 6 superscript 𝑧 1 4 minus-or-plus 𝜁 1 4 𝜋 1 2 imaginary-unit 2 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑢 2 𝑘 superscript 𝜁 2 𝑘 minus-or-plus 𝜁 1 4 𝜋 1 2 imaginary-unit 2 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑢 2 𝑘 1 superscript 𝜁 2 𝑘 1 {\displaystyle{\displaystyle\mathrm{Bi}\left(ze^{\pm\pi i/3}\right)\mathrel{% \sim}\sqrt{\frac{2}{\pi}}\frac{e^{\pm\pi i/6}}{z^{1/4}}\*\left(\cos\left(\zeta% -\tfrac{1}{4}\pi\mp\tfrac{1}{2}\mathrm{i}\ln 2\right)\sum_{k=0}^{\infty}(-1)^{% k}\frac{u_{2k}}{\zeta^{2k}}+\sin\left(\zeta-\tfrac{1}{4}\pi\mp\tfrac{1}{2}% \mathrm{i}\ln 2\right)\sum_{k=0}^{\infty}(-1)^{k}\frac{u_{2k+1}}{\zeta^{2k+1}}% \right),}}
    0 references
    DLMF:9.7.E13
    0 references
    | ph z | 2 3 π - δ phase 𝑧 2 3 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{2}{3}\pi-\delta}}
    0 references