DLMF:9.7.E8 (Q2815): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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.m1bdec

Latest revision as of 14:33, 2 January 2020

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DLMF:9.7.E8
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    Statements

    Bi ( z ) z 1 / 4 e ζ π k = 0 v k ζ k , asymptotic-expansion diffop Airy-Bi 1 𝑧 superscript 𝑧 1 4 superscript 𝑒 𝜁 𝜋 superscript subscript 𝑘 0 subscript 𝑣 𝑘 superscript 𝜁 𝑘 {\displaystyle{\displaystyle\mathrm{Bi}'\left(z\right)\sim\frac{z^{1/4}e^{% \zeta}}{\sqrt{\pi}}\sum_{k=0}^{\infty}\frac{v_{k}}{\zeta^{k}},}}
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    DLMF:9.7.E8
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    | ph z | 1 3 π - δ phase 𝑧 1 3 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{3}\pi-\delta}}
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    Bi ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    C9.S2.SS1.m2aadec
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    asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    C2.S1.SS3.p1.m11acdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aedec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2acdec
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    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    C1.S9.E7.m1acdec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C9.S1.XMD1.m1ddec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C9.S1.XMD3.m1ddec
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    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    C9.S1.XMD4.m1cdec
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    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    C9.S7.XMD1.m1ddec
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    v s subscript 𝑣 𝑠 {\displaystyle{\displaystyle v_{s}}}
    C9.S7.XMD3.m1bdec
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