DLMF:9.7.E10 (Q2817)

From DRMF
Revision as of 13:35, 29 December 2019 by Admin (talk | contribs) (‎Created a new Item: Wikidata Toolkit example test item creation)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:9.7.E10
No description defined

    Statements

    Ai ( - z ) z 1 / 4 π ( sin ( ζ - 1 4 π ) k = 0 ( - 1 ) k v 2 k ζ 2 k - cos ( ζ - 1 4 π ) k = 0 ( - 1 ) k v 2 k + 1 ζ 2 k + 1 ) , asymptotic-expansion diffop Airy-Ai 1 𝑧 superscript 𝑧 1 4 𝜋 𝜁 1 4 𝜋 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑣 2 𝑘 superscript 𝜁 2 𝑘 𝜁 1 4 𝜋 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑣 2 𝑘 1 superscript 𝜁 2 𝑘 1 {\displaystyle{\displaystyle\mathrm{Ai}'\left(-z\right)\sim\frac{z^{1/4}}{% \sqrt{\pi}}\left(\sin\left(\zeta-\tfrac{1}{4}\pi\right)\sum_{k=0}^{\infty}(-1)% ^{k}\frac{v_{2k}}{\zeta^{2k}}-\cos\left(\zeta-\tfrac{1}{4}\pi\right)\sum_{k=0}% ^{\infty}(-1)^{k}\frac{v_{2k+1}}{\zeta^{2k+1}}\right),}}
    0 references
    DLMF:9.7.E10
    0 references