DLMF:9.10.E20 (Q2905): 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: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1asdec
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.m3ardec
Property / Symbols used
 
Property / Symbols used: Q11382 / rank
 
Normal rank
Property / Symbols used: Q11382 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11382 / qualifier
 
xml-id: C9.S1.XMD2.m1edec
Property / Symbols used
 
Property / Symbols used: Q11401 / rank
 
Normal rank
Property / Symbols used: Q11401 / qualifier
 
Defining formula:

v 𝑣 {\displaystyle{\displaystyle v}}

v
Property / Symbols used: Q11401 / qualifier
 
xml-id: C9.S10.XMD4.m1dec

Latest revision as of 14:47, 2 January 2020

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DLMF:9.10.E20
No description defined

    Statements

    0 x 0 v Ai ( t ) d t d v = x 0 x Ai ( t ) d t - Ai ( x ) + Ai ( 0 ) , superscript subscript 0 𝑥 superscript subscript 0 𝑣 Airy-Ai 𝑡 𝑡 𝑣 𝑥 superscript subscript 0 𝑥 Airy-Ai 𝑡 𝑡 diffop Airy-Ai 1 𝑥 diffop Airy-Ai 1 0 {\displaystyle{\displaystyle\int_{0}^{x}\!\!\int_{0}^{v}\mathrm{Ai}\left(t% \right)\mathrm{d}t\mathrm{d}v=x\int_{0}^{x}\mathrm{Ai}\left(t\right)\mathrm{d}% t-\mathrm{Ai}'\left(x\right)+\mathrm{Ai}'\left(0\right),}}
    0 references
    DLMF:9.10.E20
    0 references
    Ai ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    C9.S2.SS1.m1akdec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1asdec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3ardec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C9.S1.XMD2.m1edec
    0 references
    v 𝑣 {\displaystyle{\displaystyle v}}
    C9.S10.XMD4.m1dec
    0 references