DLMF:9.7.E5 (Q2812): Difference between revisions

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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
 
test:

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.m2abdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
test:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1adec
Property / Symbols used
 
Property / Symbols used: Q11385 / rank
 
Normal rank
Property / Symbols used: Q11385 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11385 / qualifier
 
xml-id: C9.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11381 / rank
 
Normal rank
Property / Symbols used: Q11381 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11381 / qualifier
 
xml-id: C9.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11386 / rank
 
Normal rank
Property / Symbols used: Q11386 / qualifier
 
test:

δ 𝛿 {\displaystyle{\displaystyle\delta}}

\delta
Property / Symbols used: Q11386 / qualifier
 
xml-id: C9.S1.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: change of variable (locally) / rank
 
Normal rank
Property / Symbols used: change of variable (locally) / qualifier
 
test:

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

\zeta
Property / Symbols used: change of variable (locally) / qualifier
 
xml-id: C9.S7.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11387 / rank
 
Normal rank
Property / Symbols used: Q11387 / qualifier
 
test:

u s subscript 𝑢 𝑠 {\displaystyle{\displaystyle u_{s}}}

u_{s}
Property / Symbols used: Q11387 / qualifier
 
xml-id: C9.S7.XMD2.m1adec

Latest revision as of 13:32, 2 January 2020

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DLMF:9.7.E5
No description defined

    Statements

    test
    Ai ⁡ ( z ) ∼ e - ζ 2 ⁢ π ⁢ z 1 / 4 ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ u k ζ k , asymptotic-expansion Airy-Ai 𝑧 superscript 𝑒 𝜁 2 𝜋 superscript 𝑧 1 4 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑢 𝑘 superscript 𝜁 𝑘 {\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)\sim\frac{e^{-\zeta}}{2% \sqrt{\pi}z^{1/4}}\sum_{k=0}^{\infty}(-1)^{k}\frac{u_{k}}{\zeta^{k}},}}
    0 references
    DLMF id
    DLMF:9.7.E5
    0 references
    constraint
    | ph ⁡ z | ≤ π - δ phase 𝑧 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta}}
    0 references
    Symbols used
    Q10919
    test
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1adec
    0 references
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    Q11385
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C9.S1.XMD1.m1adec
    0 references
    Q11381
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1adec
    0 references
    Q11386
    test
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C9.S1.XMD4.m1dec
    0 references
    change of variable (locally)
    test
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C9.S7.XMD1.m1adec
    0 references
    Q11387
    test
    u s subscript 𝑢 𝑠 {\displaystyle{\displaystyle u_{s}}}
    xml-id
    C9.S7.XMD2.m1adec
    0 references
     
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