DLMF:9.12.E27 (Q2955): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Scorer function (inhomogeneous Airy function) / rank
 
Normal rank
Property / Symbols used: Scorer function (inhomogeneous Airy function) / qualifier
 
Defining formula:

Hi ⁡ ( z ) Scorer-Hi 𝑧 {\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}

\ScorerHi@{\NVar{z}}
Property / Symbols used: Scorer function (inhomogeneous Airy function) / qualifier
 
xml-id: C9.S12.E5.m2apdec

Revision as of 14:56, 2 January 2020

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DLMF:9.12.E27
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    Statements

    Defining formula
    Hi ⁡ ( z ) ∼ - 1 π ⁢ z ⁢ ∑ k = 0 ∞ ( 3 ⁢ k ) ! k ! ⁢ ( 3 ⁢ z 3 ) k , asymptotic-expansion Scorer-Hi 𝑧 1 𝜋 𝑧 superscript subscript 𝑘 0 3 𝑘 𝑘 superscript 3 superscript 𝑧 3 𝑘 {\displaystyle{\displaystyle\mathrm{Hi}\left(z\right)\sim-\frac{1}{\pi z}\sum_% {k=0}^{\infty}\frac{(3k)!}{k!(3z^{3})^{k}},}}
    0 references
    DLMF id
    DLMF:9.12.E27
    0 references
    constraint
    | ph ⁡ ( - z ) | ≤ 2 3 ⁢ π - δ phase 𝑧 2 3 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|\leq\tfrac{2}{3}% \pi-\delta}}
    0 references
    Symbols used
    Scorer function (inhomogeneous Airy function)
    Defining formula
    Hi ⁡ ( z ) Scorer-Hi 𝑧 {\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E5.m2apdec
    0 references
     
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