DLMF:9.10.E2 (Q2884): 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.m2adec

Revision as of 14:44, 2 January 2020

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DLMF:9.10.E2
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    Statements

    Defining formula
    ∫ - ∞ z Ai ⁡ ( t ) ⁢ d t = π ⁢ ( Ai ⁡ ( z ) ⁢ Hi ′ ⁡ ( z ) - Ai ′ ⁡ ( z ) ⁢ Hi ⁡ ( z ) ) , superscript subscript 𝑧 Airy-Ai 𝑡 𝑡 𝜋 Airy-Ai 𝑧 diffop Scorer-Hi 1 𝑧 diffop Airy-Ai 1 𝑧 Scorer-Hi 𝑧 {\displaystyle{\displaystyle\int_{-\infty}^{z}\mathrm{Ai}\left(t\right)\mathrm% {d}t=\pi\left(\mathrm{Ai}\left(z\right)\mathrm{Hi}'\left(z\right)-\mathrm{Ai}'% \left(z\right)\mathrm{Hi}\left(z\right)\right),}}
    0 references
    DLMF id
    DLMF:9.10.E2
    0 references
    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1aadec
    0 references
    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.m2adec
    0 references
     
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