DLMF:9.5.E8 (Q2780): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
Property / constraint
 

| ph z | < 2 3 π phase 𝑧 2 3 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\frac{2}{3}\pi}}

|\phase@@{z}|<\frac{2}{3}\pi
Property / constraint: | ph z | < 2 3 π phase 𝑧 2 3 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\frac{2}{3}\pi}} / rank
 
Normal rank

Revision as of 16:13, 30 December 2019

No description defined
Language Label Description Also known as
English
DLMF:9.5.E8
No description defined

    Statements

    Ai ( z ) = e - ζ ζ - 1 / 6 π ( 48 ) 1 / 6 Γ ( 5 6 ) 0 e - t t - 1 / 6 ( 2 + t ζ ) - 1 / 6 d t , Airy-Ai 𝑧 superscript 𝑒 𝜁 superscript 𝜁 1 6 𝜋 superscript 48 1 6 Euler-Gamma 5 6 superscript subscript 0 superscript 𝑒 𝑡 superscript 𝑡 1 6 superscript 2 𝑡 𝜁 1 6 𝑡 {\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{e^{-\zeta}\zeta^{% \ifrac{-1}{6}}}{\sqrt{\pi}(48)^{\ifrac{1}{6}}\Gamma\left(\frac{5}{6}\right)}% \int_{0}^{\infty}e^{-t}t^{-\ifrac{1}{6}}\left(2+\frac{t}{\zeta}\right)^{-% \ifrac{1}{6}}\mathrm{d}t,}}
    0 references
    0 references
    | ph z | < 2 3 π phase 𝑧 2 3 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\frac{2}{3}\pi}}
    0 references