DLMF:9.10.E18 (Q2901): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2agdec

Revision as of 14:47, 2 January 2020

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DLMF:9.10.E18
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    Statements

    Ai ( z ) = 3 z 5 / 4 e - ( 2 / 3 ) z 3 / 2 4 π 0 t - 3 / 4 e - ( 2 / 3 ) t 3 / 2 Ai ( t ) z 3 / 2 + t 3 / 2 d t , Airy-Ai 𝑧 3 superscript 𝑧 5 4 superscript 𝑒 2 3 superscript 𝑧 3 2 4 𝜋 superscript subscript 0 superscript 𝑡 3 4 superscript 𝑒 2 3 superscript 𝑡 3 2 Airy-Ai 𝑡 superscript 𝑧 3 2 superscript 𝑡 3 2 𝑡 {\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{3z^{5/4}e^{-(2/3)z% ^{3/2}}}{4\pi}\*\int_{0}^{\infty}\frac{t^{-3/4}e^{-(2/3)t^{3/2}}\mathrm{Ai}% \left(t\right)}{z^{3/2}+t^{3/2}}\mathrm{d}t,}}
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    DLMF:9.10.E18
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    | ph z | < 2 3 π phase 𝑧 2 3 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{2}{3}\pi}}
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    Ai ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    C9.S2.SS1.m1aidec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2agdec
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