DLMF:9.5.E6 (Q2778): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: exponential function / rank
 
Normal rank
Property / Symbols used: exponential function / qualifier
 
Defining formula:

exp z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}

\exp@@{\NVar{z}}
Property / Symbols used: exponential function / qualifier
 
xml-id: C4.S2.E19.m2acdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aedec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
Defining formula:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1adec
Property / Symbols used
 
Property / Symbols used: Q11381 / rank
 
Normal rank
Property / Symbols used: Q11381 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11381 / qualifier
 
xml-id: C9.S1.XMD3.m1bdec

Latest revision as of 14:25, 2 January 2020

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DLMF:9.5.E6
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    Statements

    Ai ( z ) = 3 2 π 0 exp ( - t 3 3 - z 3 3 t 3 ) d t , Airy-Ai 𝑧 3 2 𝜋 superscript subscript 0 superscript 𝑡 3 3 superscript 𝑧 3 3 superscript 𝑡 3 𝑡 {\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{\sqrt{3}}{2\pi}% \int_{0}^{\infty}\exp\left(-\frac{t^{3}}{3}-\frac{z^{3}}{3t^{3}}\right)\mathrm% {d}t,}}
    0 references
    DLMF:9.5.E6
    0 references
    | ph z | < 1 6 π phase 𝑧 1 6 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{6}\pi}}
    0 references
    Ai ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    C9.S2.SS1.m1acdec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aedec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aedec
    0 references
    exp z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    C4.S2.E19.m2acdec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aedec
    0 references
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    C1.S9.E7.m1adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C9.S1.XMD3.m1bdec
    0 references