DLMF:9.9.E7 (Q2868): 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: 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.m2aedec
Property / Symbols used
 
Property / Symbols used: Q11394 / rank
 
Normal rank
Property / Symbols used: Q11394 / qualifier
 
Defining formula:

a k zero-Airy-Ai 𝑘 {\displaystyle{\displaystyle a_{\NVar{k}}}}

\zAirya{\NVar{k}}
Property / Symbols used: Q11394 / qualifier
 
xml-id: C9.S9.SS1.p1.m5addec
Property / Symbols used
 
Property / Symbols used: Q11385 / rank
 
Normal rank
Property / Symbols used: Q11385 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11385 / qualifier
 
xml-id: C9.S1.XMD1.m1fdec
Property / Symbols used
 
Property / Symbols used: expansion (locally) / rank
 
Normal rank
Property / Symbols used: expansion (locally) / qualifier
 
Defining formula:

V 𝑉 {\displaystyle{\displaystyle V}}

V
Property / Symbols used: expansion (locally) / qualifier
 
xml-id: C9.S9.XMD4.m1dec

Latest revision as of 14:41, 2 January 2020

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DLMF:9.9.E7
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    Statements

    Ai ( a k ) = ( - 1 ) k - 1 V ( 3 8 π ( 4 k - 1 ) ) , diffop Airy-Ai 1 zero-Airy-Ai 𝑘 superscript 1 𝑘 1 𝑉 3 8 𝜋 4 𝑘 1 {\displaystyle{\displaystyle\mathrm{Ai}'\left(a_{k}\right)=(-1)^{k-1}V\left(% \tfrac{3}{8}\pi(4k-1)\right),}}
    0 references
    DLMF:9.9.E7
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    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
    a k zero-Airy-Ai 𝑘 {\displaystyle{\displaystyle a_{\NVar{k}}}}
    C9.S9.SS1.p1.m5addec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C9.S1.XMD1.m1fdec
    0 references
    V 𝑉 {\displaystyle{\displaystyle V}}
    C9.S9.XMD4.m1dec
    0 references