DLMF:9.12.E13 (Q2941): Difference between revisions

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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.m1jdec

Latest revision as of 14:53, 2 January 2020

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DLMF:9.12.E13
No description defined

    Statements

    Defining formula
    Gi ⁡ ( z ) = e ∓ π ⁢ i / 3 ⁢ Hi ⁡ ( z ⁢ e ± 2 ⁢ π ⁢ i / 3 ) ± i ⁢ Ai ⁡ ( z ) , Scorer-Gi 𝑧 plus-or-minus superscript 𝑒 minus-or-plus 𝜋 𝑖 3 Scorer-Hi 𝑧 superscript 𝑒 plus-or-minus 2 𝜋 𝑖 3 𝑖 Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Gi}\left(z\right)=e^{\mp\pi i/3}\mathrm{Hi% }\left(ze^{\pm 2\pi i/3}\right)\pm i\mathrm{Ai}\left(z\right),}}
    0 references
    DLMF id
    DLMF:9.12.E13
    0 references
    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1aedec
    0 references
    Scorer function (inhomogeneous Airy function)
    Defining formula
    Gi ⁡ ( z ) Scorer-Gi 𝑧 {\displaystyle{\displaystyle\mathrm{Gi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E4.m2ahdec
    0 references
    Scorer function (inhomogeneous Airy function)
    Defining formula
    Hi ⁡ ( z ) Scorer-Hi 𝑧 {\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E5.m2aidec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
    0 references
    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1jdec
    0 references
     
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