DLMF:9.13.E9 (Q2971): 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: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
test:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2abdec
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.m1gdec
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: parameter (locally) / rank
 
Normal rank
Property / Symbols used: parameter (locally) / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: parameter (locally) / qualifier
 
xml-id: C9.S13.XMD1.m1gdec
Property / Symbols used
 
Property / Symbols used: Q11414 / rank
 
Normal rank
Property / Symbols used: Q11414 / qualifier
 
test:

p 𝑝 {\displaystyle{\displaystyle p}}

p
Property / Symbols used: Q11414 / qualifier
 
xml-id: C9.S13.XMD3.m1gdec
Property / Symbols used
 
Property / Symbols used: Q11415 / rank
 
Normal rank
Property / Symbols used: Q11415 / qualifier
 
test:

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

\zeta
Property / Symbols used: Q11415 / qualifier
 
xml-id: C9.S13.XMD4.m1edec

Latest revision as of 13:59, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:9.13.E9
No description defined

    Statements

    test
    A n ⁡ ( z ) = p / π ⁢ sin ⁡ ( p ⁢ π ) ⁢ z - n / 4 ⁢ e - ζ ⁢ ( 1 + O ⁡ ( ζ - 1 ) ) , ODE-generalized-Airy-A 𝑛 𝑧 𝑝 𝜋 𝑝 𝜋 superscript 𝑧 𝑛 4 superscript 𝑒 𝜁 1 Big-O superscript 𝜁 1 {\displaystyle{\displaystyle A_{n}\left(z\right)=\sqrt{\ifrac{p}{\pi}}\sin% \left(p\pi\right)z^{-n/4}e^{-\zeta}\left(1+O\left(\zeta^{-1}\right)\right),}}
    0 references
    DLMF id
    DLMF:9.13.E9
    0 references
    constraint
    | ph ⁡ z | ≤ 3 ⁢ p ⁢ π - δ phase 𝑧 3 𝑝 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq 3p\pi-\delta}}
    0 references
    Symbols used
    order not exceeding
    test
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
    0 references
    Q11416
    test
    A n ⁡ ( z ) ODE-generalized-Airy-A 𝑛 𝑧 {\displaystyle{\displaystyle A_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C9.S13.SS1.p2.m3aedec
    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
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2abdec
    0 references
    Q11381
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1gdec
    0 references
    Q11386
    test
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C9.S1.XMD4.m1dec
    0 references
    parameter (locally)
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C9.S13.XMD1.m1gdec
    0 references
    Q11414
    test
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C9.S13.XMD3.m1gdec
    0 references
    Q11415
    test
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C9.S13.XMD4.m1edec
    0 references
     
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