DLMF:9.10.E13 (Q2896): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(2 intermediate revisions by the same user not shown)
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.m3aldec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11400 / rank
 
Normal rank
Property / Symbols used: Q11400 / qualifier
 
Defining formula:

p 𝑝 {\displaystyle{\displaystyle p}}

p
Property / Symbols used: Q11400 / qualifier
 
xml-id: C9.S10.XMD2.m1dec

Latest revision as of 14:46, 2 January 2020

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DLMF:9.10.E13
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    Statements

    - e p t Ai ( t ) d t = e p 3 / 3 , superscript subscript superscript 𝑒 𝑝 𝑡 Airy-Ai 𝑡 𝑡 superscript 𝑒 superscript 𝑝 3 3 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}e^{pt}\mathrm{Ai}\left(t% \right)\mathrm{d}t=e^{p^{3}/3},}}
    0 references
    DLMF:9.10.E13
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    p > 0 𝑝 0 {\displaystyle{\displaystyle\Re p>0}}
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    Ai ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    C9.S2.SS1.m1aedec
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aldec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aldec
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    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1adec
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    p 𝑝 {\displaystyle{\displaystyle p}}
    C9.S10.XMD2.m1dec
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