DLMF:9.7.E18 (Q2827): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11391 / rank
 
Normal rank
Property / Symbols used: Q11391 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11391 / qualifier
 
xml-id: C9.S7.XMD11.m1dec

Revision as of 14:36, 2 January 2020

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DLMF:9.7.E18
No description defined

    Statements

    test
    Ai ⁡ ( z ) = e - ζ 2 ⁢ π ⁢ z 1 / 4 ⁢ ( ∑ k = 0 n - 1 ( - 1 ) k ⁢ u k ζ k + R n ⁢ ( z ) ) , Airy-Ai 𝑧 superscript 𝑒 𝜁 2 𝜋 superscript 𝑧 1 4 superscript subscript 𝑘 0 𝑛 1 superscript 1 𝑘 subscript 𝑢 𝑘 superscript 𝜁 𝑘 subscript 𝑅 𝑛 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{e^{-\zeta}}{2\sqrt% {\pi}z^{1/4}}\left(\sum_{k=0}^{n-1}(-1)^{k}\frac{u_{k}}{\zeta^{k}}+R_{n}(z)% \right),}}
    0 references
    DLMF id
    DLMF:9.7.E18
    0 references
    Symbols used
    Q10919
    test
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aodec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
    0 references
    Q11385
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C9.S1.XMD1.m1kdec
    0 references
    Q11381
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1ldec
    0 references
    change of variable (locally)
    test
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C9.S7.XMD1.m1ldec
    0 references
    Q11391
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C9.S7.XMD11.m1dec
    0 references
     
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