DLMF:9.7.E19 (Q2828): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: change of variable (locally) / rank
 
Normal rank
Property / Symbols used: change of variable (locally) / qualifier
 
Defining formula:

ζ 𝜁 {\displaystyle{\displaystyle\zeta}}

\zeta
Property / Symbols used: change of variable (locally) / qualifier
 
xml-id: C9.S7.XMD1.m1mdec
Property / Symbols used
 
Property / Symbols used: Q11391 / rank
 
Normal rank
Property / Symbols used: Q11391 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11391 / qualifier
 
xml-id: C9.S7.XMD11.m1adec
Property / Symbols used
 
Property / Symbols used: remainder function (locally) / rank
 
Normal rank
Property / Symbols used: remainder function (locally) / qualifier
 
Defining formula:

S n subscript 𝑆 𝑛 {\displaystyle{\displaystyle S_{n}}}

S_{n}
Property / Symbols used: remainder function (locally) / qualifier
 
xml-id: C9.S7.XMD13.m1dec
Property / Symbols used
 
Property / Symbols used: Q11388 / rank
 
Normal rank
Property / Symbols used: Q11388 / qualifier
 
Defining formula:

v s subscript 𝑣 𝑠 {\displaystyle{\displaystyle v_{s}}}

v_{s}
Property / Symbols used: Q11388 / qualifier
 
xml-id: C9.S7.XMD3.m1fdec

Latest revision as of 14:36, 2 January 2020

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DLMF:9.7.E19
No description defined

    Statements

    Defining formula
    Ai ′ ⁡ ( z ) = - z 1 / 4 ⁢ e - ζ 2 ⁢ π ⁢ ( ∑ k = 0 n - 1 ( - 1 ) k ⁢ v k ζ k + S n ⁢ ( z ) ) , diffop Airy-Ai 1 𝑧 superscript 𝑧 1 4 superscript 𝑒 𝜁 2 𝜋 superscript subscript 𝑘 0 𝑛 1 superscript 1 𝑘 subscript 𝑣 𝑘 superscript 𝜁 𝑘 subscript 𝑆 𝑛 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}'\left(z\right)=-\frac{z^{1/4}e^{-\zeta% }}{2\sqrt{\pi}}\left(\sum_{k=0}^{n-1}(-1)^{k}\frac{v_{k}}{\zeta^{k}}+S_{n}(z)% \right),}}
    0 references
    DLMF id
    DLMF:9.7.E19
    0 references
    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1afdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2apdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aidec
    0 references
    Q11385
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C9.S1.XMD1.m1ldec
    0 references
    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1mdec
    0 references
    change of variable (locally)
    Defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C9.S7.XMD1.m1mdec
    0 references
    Q11391
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C9.S7.XMD11.m1adec
    0 references
    remainder function (locally)
    Defining formula
    S n subscript 𝑆 𝑛 {\displaystyle{\displaystyle S_{n}}}
    xml-id
    C9.S7.XMD13.m1dec
    0 references
    Q11388
    Defining formula
    v s subscript 𝑣 𝑠 {\displaystyle{\displaystyle v_{s}}}
    xml-id
    C9.S7.XMD3.m1fdec
    0 references
     
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