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: Q11381 / rank
 
Normal rank
Property / Symbols used: Q11381 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11381 / qualifier
 
xml-id: C9.S1.XMD3.m1ddec

Revision as of 14:33, 2 January 2020

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DLMF:9.7.E8
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    Statements

    Defining formula
    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}},}}
    0 references
    DLMF id
    DLMF:9.7.E8
    0 references
    constraint
    | ph ⁡ z | ≤ 1 3 ⁢ π - δ phase 𝑧 1 3 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{3}\pi-\delta}}
    0 references
    Symbols used
    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2aadec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1acdec
    0 references
    Q11385
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C9.S1.XMD1.m1ddec
    0 references
    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1ddec
    0 references
     
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