DLMF:9.13.E11 (Q2973): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11417 / rank
 
Normal rank
Property / Symbols used: Q11417 / qualifier
 
test:

B n ⁡ ( z ) ODE-generalized-Airy-B 𝑛 𝑧 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{z}\right)}}

\genAiryODEB{\NVar{n}}@{\NVar{z}}
Property / Symbols used: Q11417 / qualifier
 
xml-id: C9.S13.SS1.p2.m4aedec
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.m2addec
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.m2abdec
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.m1abdec
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.m1idec
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.m1bdec
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.m1idec
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.m1idec
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.m1gdec

Latest revision as of 14:00, 2 January 2020

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English
DLMF:9.13.E11
No description defined

    Statements

    test
    B n ⁡ ( z ) = π - 1 / 2 ⁢ z - n / 4 ⁢ e ζ ⁢ ( 1 + O ⁡ ( ζ - 1 ) ) , ODE-generalized-Airy-B 𝑛 𝑧 superscript 𝜋 1 2 superscript 𝑧 𝑛 4 superscript 𝑒 𝜁 1 Big-O superscript 𝜁 1 {\displaystyle{\displaystyle B_{n}\left(z\right)={\pi}^{-1/2}z^{-n/4}e^{\zeta}% \left(1+O\left(\zeta^{-1}\right)\right),}}
    0 references
    DLMF id
    DLMF:9.13.E11
    0 references
    constraint
    | ph ⁡ z | ≤ p ⁢ π - δ phase 𝑧 𝑝 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq p\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.m2abdec
    0 references
    Q11417
    test
    B n ⁡ ( z ) ODE-generalized-Airy-B 𝑛 𝑧 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C9.S13.SS1.p2.m4aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1abdec
    0 references
    Q11381
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1idec
    0 references
    Q11386
    test
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C9.S1.XMD4.m1bdec
    0 references
    parameter (locally)
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C9.S13.XMD1.m1idec
    0 references
    Q11414
    test
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C9.S13.XMD3.m1idec
    0 references
    Q11415
    test
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C9.S13.XMD4.m1gdec
    0 references
     
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